Methods of Savings Money wisely invested grows over time. (credit: “Stack of Cash” by Janak Raja/Flickr, Public Domain Mark 1.0) Learning Objectives After completing this section, you should be able to: Distinguish various basic forms of savings plans. Compute return on investment for basic forms of savings plans. Compute payment to reach a financial goal. The stock market crash of 1929 led to the Great Depression, a decade-long global downturn in productivity and employment. A state of shock swept through the United States; the damage to people’s lives was immeasurable. Americans no longer trusted established financial institutions. By October 1931, the banking industry’s biggest challenge was restoring confidence to the American public. In the next 10 years, the federal government would impose strict regulations and guidelines on the financial industry. The Emergency Banking Act of 1933 created the Federal Deposit Insurance Corporation (FDIC), which insures bank deposits. The new federal guidelines helped ease suspicions among the general public about the banking industry. Gradually, things returned to normal, and today we have more investment instruments, many insured through the FDIC, than ever before. In this section, we will first look at the different types of savings accounts and proceed to discuss the various types of investments. There is some overlap, but we will try to differentiate among these financial instruments. Saving money should be a goal of every adult, but it can also be a difficult goal to attain. Distinguish Various Basic Forms of Savings Plans There are at least three types of savings accounts. Traditional savings accounts, certificates of deposit (CDs), and money market accounts are three main savings account vehicles. Savings Account A savings account is probably the most well-known type of investment, and for many people it is their first experience with a bank. A savings account is a deposit account, held at a bank or other financial institution, which bears some interest on the deposited money. Savings accounts are intended as a place to save money for emergencies or to achieve short-term goals. They typically pay a low interest rate, but there is virtually no risk involved, and they are insured by the FDIC for up to $250,000. Savings accounts have some strengths. They are highly flexible. Generally, there are no limitations on the number of withdrawals allowed and no limit on how much you can deposit. It is not unusual, however, that a savings account will have a minimum balance in order for the bank to pay maintenance costs. If your account should dip below the minimum, there are usually fees attached. Many banks are covered by FDIC insurance. The FDIC is the Federal Deposit Insurance Corporation and is an independent agency created by the U.S. Congress. One of its purposes is to provide insurance for deposits in banks, including savings accounts. Be aware, not all banks are FDIC insured. The FDIC insures up to $250,000 for a savings account, so you do not want your balance to exceed that federally insured limit. Having your savings account at the same bank as your checking account does offer a real advantage. For example, if your checking account is approaching its lower limit, you can transfer funds from your savings account and avoid any bank fees. Similarly, if you have an excess of funds in your checking account, you can transfer funds to your savings account and earn some interest. Checking accounts rarely pay interest. J.P. Morgan J.P. Morgan was a wealthy banker around the turn of the 20th century. His business interests included railroads and the steel industry. However, it was in 1907 that a financial crisis, caused by poor banking decisions and followed by such great distrust in the banking system that a frenzy of withdrawals from banks occurred, that J.P. Morgan and other wealthy bankers lent from their own funds to help stabilize and save the system. There are some weaknesses to savings accounts. Primarily, it is because savings accounts earn very low interest rates. This means they are not the best way to grow your money. Experts, though, recommend keeping a savings account balance to cover 3 to 6 months of living expenses in case you should lose your job, have a sudden medical expense, or other emergency. Around tax time, you will receive a 1099-INT form stating the amount of interest earned on your savings, which is the amount that must be reported when you file your tax return. A 1099 form is a tax form that reports earnings that do not come from your employer, including interest earned on savings accounts. These 1099 forms have the suffix INT to indicate that the income is interest income. Savings accounts earn interest, and those earnings can be found using the interest formulas from previous sections. The final value of these accounts is sometimes called the future value of the account. Single Deposit in a Savings Account Violet deposits $4,520.00 in a savings account bearing 1.45% interest compounded annually. If she does not add to or withdraw any of that money, how much will be in the account after 3 years? To find the compound interest, use the formula from Compound Interest , A = P ( 1 + r n ) n t , where A represents the amount in the account after t years, with initial deposit (or principal) of P , at an annual interest rate, in decimal form, of r , compounded n times per year. Violet has a principal of $4,520.00, which will earn an interest of r = 0.0145, compounded yearly (so n = 1), for t = 3 years. Substituting and calculating, we find that Violet’s account will be worth A = P ( 1 + r n ) n t = $ 4,520.00 ( 1 + 0.0145 1 ) 1 × 3 = $ 4,520.00 ( 1.0145 ) 3 = $ 4,719.48 Or, Violet will have $4,719.48 after 3 years. Banks have not always offered interest on savings accounts. An 1836 publication from Indiana noted that banks in other states allow small interest on deposits. It specifically says that in these other states, these deposits are what business transactions are based upon. And that giving interest would encourage deposits, and thus increase the business that banks can do. Journal of the House of Representatives of the Sate of Indiana Certificates of Deposit, or CDs We discussed certificates of deposit (CDs) in earlier sections. CDs differ from savings accounts in a few ways. First, the investment lasts for a fixed period of time, agreed to when the money is invested in the CD. These time periods often range from 6 months to 5 years. Money from the CD cannot be withdrawn (without penalty) until the investment period is up. Also, money cannot be added to an existing CD. Certificates of deposit have features similar to savings accounts. They are insured by the FDIC. They are entirely safe. They do, though, offer a better interest rate. The trade-off is that once the money is invested in a CD, that money is unavailable until the investment period ends. 5-Year CD Silvio deposits $10,000 in a CD that yields 2.17% compounded semiannually for 5 years. How much is the CD worth after 5 years? This also uses the compound interest formula from Compound Interest , A = P ( 1 + r n ) nt , Substituting the values P = $10,000, r = 0.0217, n = 2 (semiannually means twice per year), and t = 5, we find the account will be worth A = P ( 1 + r n ) nt = $ 10 , 000.00 ( 1 + 0.0217 2 ) 2 × 5 = $ 10,000.00 ( 1.01085 ) 10 = $ 11 , 239.53 The CD will be worth $11,219.53 after 5 years. Money Market Account A money market account is similar to a savings account, except the number of transactions (withdrawals and transfers) is generally limited to six each month. Money market accounts typically have a minimum balance that must be maintained. If the balance in the account drops below the minimum, there is likely to be a penalty. Money market accounts offer the flexibility of checks and ATM cards. Finally, the interest rate on a money market account is typically higher than the interest rate on a savings account. Single Deposit to a Money Market Account Marietta opens a money market account, and deposits $2,500.00 in the account. It bears 1.76% interest compounded monthly. If she makes no other transactions on the account, how much will be in the account after 4 years? This, once again, uses the compound interest formula from Compound Interest : A = P ( 1 + r n ) nt , Substituting the values P = $25,000, r = 0.0176, n = 12, and t = 4, we find the account will be worth A = P ( 1 + r n ) nt = $ 2,500.00 ( 1 + 0.0176 12 ) 12 × 4 = $ 2,500.00 ( 1.0014 6 ¯ ) 48 = $ 2,682.20 The money market account will be worth $2,682.20 after 4 years. Return on Investment If we want to compare the profitability of different investments, like savings accounts versus other investment tools, we need a measure that evens the playing field. Such a measure is return on investment . The return on investment, often denoted ROI, is the percent difference between the initial investment, P , and the final value of the investment, F V , or ROI = F V - P P , expressed as a percentage. The length of time of the investment is not considered in ROI. Calculating Return on Investment Determine the return on investment for the 5-year CD from . Round the percentage to two decimal places. Determine the return on investment for the money market account from . Round the percentage to two decimal places. The initial deposit in the CD was $10,000, so P = $10,000. The value at the end of 5 years was $11,239.53. so F V = $11,239.53. Substituting and computing we find the return on investment. ROI = F V - P P = $ 11,239.53 - $ 10,000 $ 10,000 = $ 1,239.53 $ 10 , 000 = 0.123953 The ROI is 12.40%. The initial deposit in the money market was $2,500, so P = $2,500. The value at the end of 4 years was $2,682.20. so F V = $2,682.20. Substituting and computing we find the return on investment. ROI = F V - P P = $ 2,682.20 - $ 2,500 $ 2,500 = $ 182.20 $ 2,500 = 0.07288 The ROI is 7.29%. Return on Investment, ROI Annuities as Savings In Compound Interest , we talked about the future value of a single deposit. In reality, people often open accounts that allow them to add deposits, or payments , to the account at regular intervals. This agrees with the 50-30-20 budget philosophy, where some income is saved every month. When a deposit is made at the end of each compounding period, such a savings account is called an ordinary annuity . The formula for the future value of an ordinary annuity is F V = pmt × ( 1 + r / n ) n × t - 1 r / n , where F V is the future value of the annuity, pmt is the payment, r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the number of years. It is important to note that the number of deposits per year and the number of periods per year are the same. Another form of annuity if the annuity due, which has deposits at the start of each compounding period. This other annuity type has different formulas and is not addressed in this text. Future Value of an Ordinary Annuity Jill has an account that bears 3.75% interest compounded monthly. She decides to deposit $250.00 each month, at the end of the compounding period, into this account. What is the future value of this account, after 8 years? These are regular payments into an account bearing compound interest. She is depositing them at the end of each compounding period. This makes this an ordinary annuity. Substituting the values pmt = 250, r = 0.0375, n = 12, and t = 8 into the formula, we find the future value of the account. F V = pmt × ( 1 + r / n ) n × t - 1 r / n = 250 × ( 1 + 0.0375 / 12 ) 12 × 8 - 1 0.0375 / 12 = 250 × ( 1.003125 ) 96 - 1 0.003125 = 250 × 1.34922752406 - 1 0.003125 = 250 × 0.34922752406 0.003125 = 250 × 111.752807699 = 27 , 938.202 The account, after 8 years, will contain $27,938.20. Setting Savings Account Interest Rates There are a number of factors that contribute to the amount a bank gives for savings accounts. The interest rate reflects how much the bank values deposits. It also reflects the money that the bank will earn when they lend out money. Finally, interest rates are impacted by the Federal Reserve Bank. When the Fed raises interest rates, so do banks. The Federal Reserve Chairperson The Federal Reserve Board monitors the risks in the financial system to help ensure a healthy economy for individuals, companies, and communities. The Board oversees the 12 regional reserve banks. The Chairperson of the Federal Reserve Board testifies to Congress twice per year, meets with the secretary of the Treasury, chairs the Federal Open Market Committee, and is the face of federal monetary policy. Currently, the Fed Chair is Jerome Powell, who has served since 2018. Saving for College When Yusef was born, Rita and George began to save for Yusef’s college years by investing $2,500 each year in a savings account bearing 3.4% interest compounded annually. How much will they have saved after 18 years? To find the future value of the account, we use the ordinary annuity formula F V = pmt × ( 1 + r / n ) n × t - 1 r / n . The payment is $2,500, rate is 0.034, the number of compounding periods is 1, and the number of years is 18. Substituting these values and computing, we have F V = pmt × ( 1 + r / n ) n × t - 1 r / n = $ 2,500 × ( 1 + 0.034 / 1 ) 1 × 18 - 1 0.034 / 1 = $ 2,500 × ( 1.034 ) 18 - 1 0.034 = $ 2,500 × 1.82544897331 - 1 0.034 = $ 2,500 × 24.2779109798 = $ 60,694.77 After saving for 18 years, Rita and George will have $60,694.77 for Yusef’s college. Google Sheets offers a function to calculate the future value of an ordinary annuity. To get Google Sheets to calculate the future value, you use the following: =fv(rate,number_of_periods, payment, present_value, end_or_beginning). To explain, the rate is the rate per compounding period. From our formula, that is r / n . Also, the number of periods must be entered. From our formula, that is n × t . The payment is the amount deposited each period. Present value is 0 if we begin with no money and rely only on the payments to be made. However, if some money is available to put in the account before the payments start, that amount, an initial deposit, would be the value of P V . Finally, for an ordinary annuity, enter 0 for end or beginning. Using the values for Jill, the payment amount is $250, r = 0.0375, n = 12, t = 8, and that there is no initial deposit, P V = 0, the Google Sheets formula is =fv(0.0375/12,12*8,250,0,0). shows the formula in Google Sheets. Google Sheets formula Hitting the enter key shows the payment value ( ). Payment value Notice that the future value is negative, since it is a payment leaving an account. Future Value Using Google Sheets Compute Payment to Reach a Financial Goal The formula used to get the future value of an ordinary annuity is useful, finding out what the final amount in the account will be. However, that isn’t how planning works. To plan, we need to know how much to put into the ordinary annuity each compounding period in order to reach a goal. Fortunately, that formula exists. The formula for the amount that needs to be deposited per period, pmt , of an ordinary annuity to reach a specified goal, FV , is pmt = F V × ( r / n ) ( 1 + r / n ) n × t - 1 , where r is the annual interest rate (in decimal form), n is the number of periods per year, and t is the number of years. With this formula, it is possible to plan the amount to be saved. Saving for a Car Yaroslava wants to save in order to buy a car, in 3 years, without taking out a loan. She determines that she’ll need $35,500 for the purchase. If she deposits money into an ordinary annuity that yields 4.25% interest compounded monthly, how much will she need to deposit each month? Yaroslava has a goal and needs to know the payments to make to reach the goal. Her goal is FV = $35,500, with an interest rate r = 0.0425, compounded per month so n = 12, and for 3 years, making t = 3. Substituting into the formula, Yaroslava finds the necessary payment. pmt = F V × ( r / n ) ( 1 + r / n ) n × t - 1 = 35,500 × ( 0.0425 / 12 ) ( 1 + 0.0425 / 12 ) 12 × 3 - 1 = 35,500 × ( 0.003541 6 ¯ ) ( 1.003541 6 ¯ ) 36 - 1 = 125.7291 6 ¯ 0.13572901696 = 926.325 To reach her goal, Yaroslava would need to deposit $926.33 in her account each month. This has been rounded up, so that the deposits don’t fall short of the goal. However, some round off using the standard rounding rules: if the last digit is 1, 2, 3, or 4, the number is rounded down; if the last digit is 5, 6, 7, 8, or 9 the number is rounded up. Google Sheets offers a function to calculate the payment necessary to reach a goal using ordinary annuities. To get Google Sheets to calculate the payment, you use the following: =pmt(rate,number_of_periods, present_value, future_value, end_or_beginning). To explain, the rate is per compounding period. From our formula, that is r / n . Also, the number of periods must be entered. From our formula, that is n × t . The present value is the amount of money that the account begins with. If we begin with no money and rely only on the payments to be made, then this number is 0. However, if some money is available to put in the account before the payments start, that amount, an initial deposit, would be the value of P V . Next, enter the future value, F V . Finally, for an ordinary annuity, enter 0 for end or beginning. Using the values for Yaroslava, r = 0.0425, n = 12, t = 3, and that there is no initial deposit, P V = 0, the Google Sheets formula is =pmt(0.0425/12,12*3,0,35500,0). shows the formula in Google Sheets. Google Sheets formula Hitting the enter key shows the payment value ( ). Payment value Notice that the payment is negative, since it is a payment leaving an account. Additionally, the payment is $926.32. We rounded that up, but Google Sheets rounded off. Check Your Understanding Key Terms Savings account 1099 form Certificate of deposit Money market account Return on investment Ordinary annuity Key Concepts There are three main types of savings accounts, saving accounts, certificates of deposit (CD), and money market accounts. Savings account are very risk free, and so yield low interest rates. The differences in the three types of savings accounts relate to their convenience. Savings account typically have a lower interest rate that money market accounts, which typically have lower interest rates than CDs. Ordinary annuities more accurately reflect how we save, in that money is deposited repeatedly over time. Spreadsheet software, such as Google Sheets, have built in functions that can be used to quickly calculate both the future value of an ordinary annuity account, but also the payment necessary to reach a goal using an ordinary annuity. Videos Return on Investment, ROI Future Value Using Google Sheets Formulas A = P ( 1 + r n ) n t ROI = F V - P P F V = p m t × ( 1 + r / n ) n × t - 1 r / n p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1

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Investments Stocks are bought and sold to improve investment values. (credit: modification of work "FT ringing the Closing Bell at the NYSE" by Financial Times/Flickr, CC BY 2.0) Learning Objectives After completing this section, you should be able to: Distinguish between basic forms of investments including stocks, bonds, and mutual funds. Understand what bonds are and how bond investments work. Understand how stocks are purchased and gain or lose value. Read and derive information from a stock table. Define a mutual fund and how to invest. Compute return on investment for basic forms of investments. Compute future value of investments. Compute payment to reach a financial goal. Identify and distinguish between retirement savings accounts. You can save your money in a safe or a vault (or worse, under the mattress!), but that money does not grow. It would be hard to save enough for retirement that way. What can be done to increase the value of the money you already have? The answer is to invest it. Use the money that you have to earn more money back. For instance, as we saw in Methods of Savings , you can save it in a bank. Or, to reach loftier goals, invest in something more likely to grow, such as stocks. A great example of this is Apple stock. Anyone who bought stock in Apple Inc. (formerly Apple Computer, Inc.) in 1997 and held onto the shares earned a lot of money. To be more specific, $100 worth of Apple shares bought in 1980, when it was first sold to the public, was valued at $67,564 in 2019, or 676 times more! Perhaps you have heard a story like that, of an investment opportunity taken that paid off, or the story of an investment opportunity missed. But such stories are the exceptions. In this section, we’ll investigate bonds, stocks, and mutual funds and their comparative strengths and weaknesses. We close the section with a discussion of retirement savings accounts. Distinguish Between Basic Forms of Investments Bonds, stocks, and mutual funds tend to offer higher returns, but to varying degrees, come with higher risks. Stocks and mutual funds also vary in how much they earn. Their predicted rates of return on investment are not guaranteed, but educated guesses based on market trends and historical performance. We will use the methods and formulas we learned earlier to evaluate these forms of investment. Bonds Bonds are issued from big companies and from governments. Selling bonds is an alternative to an institution taking a loan from a bank. The funds from the selling of bonds are often used for large projects, like funding the building of a new highway or hospital. Bonds are considered a conservative investment. They are bought for what is known as the issue price . The interest is fixed (does not change) at the time of purchase and is based on the issue price of the bond. The interest rate is often referred to as the coupon rate; the interest paid is often called the coupon yield. The interest paid is often higher than savings accounts and the risk is exceptionally low. The bond is for a fixed length of time. The end of this time is the maturity date of the bond. There are several types of bonds: Treasury bonds are issued by the federal government. Municipal bonds are issued by state and local governments. Corporate bonds are issued by major corporations. There are other types of bonds available, but they are beyond the scope of this section. Trading Bonds Bonds are often part of larger investment portfolios. These bonds may be traded. However, the interest paid is based on the price when the bond was bought (the issue price). These bonds can be bought and sold for more or less money than the issue price. If the bond is bought for more than the issue price, the interest is still paid on the issue price, not on the purchase price when the trade was made. This means the actual return on the bond decreases. If the bond is bought for less than the issue price, the return on the bond goes up. Bonds Bond Investment Muriel purchases a $3,000 bond with a maturity of 4 years at a fixed coupon rate of 5.5% paid annually. How much is Muriel paid each year, and how much does she receive on the maturity date? The coupon rate is 5.5%. 5.5% of her bond value is 0.055 × $ 3,000 = $ 165 . After year 1, Muriel receives $165. She receives $165 after years 2 and 3 also. In year 4, when the bond matures, Muriel receives $3,165, or the interest and the initial investment, or principal. Stocks Stocks are part ownership in a company. They come in units called shares . The performance and earnings of stocks is not guaranteed, which makes them riskier than any other investment discussed earlier. However, they can offer higher return on investment than the other investments. Their value grows in two ways. They offer dividends , which is a portion of the profit made by the company. And the price per share can increase based on how others see that value of the company changing. If the value of the company drops, or the company folds, the money invested in the stock also drops. Most stock transactions are executed through a broker. Brokers’ commissions can be a percentage of value of the trades made or a flat fee. There are full-service brokers who charge higher commission rates, but they also offer financial advice and perform the research that you may not have the time or the expertise to do on your own. A discount broker only executes the stock transactions, buying or selling, so they charge lower rates than full-service brokers. There are also brokers that offer commission-free trading. An important thing to remember is that stocks might provide a very large return on investment, but the trade-off is the risk associated with owning stocks. Chapter 11 Bankruptcy and Stocks In the fall of 2022, the parent company of Regal Theaters, named Cineworld, filed for Chapter 11 bankruptcy. According to news articles, the bankruptcy was necessitated due to its heavy debt load. Generally, a company can file for Chapter 11 bankruptcy to allow them time to reorganize and restructure debts. When this happens, the company, after the Chapter 11 process is over, offers new stock. This makes the previous stock worthless. However, the company may allow an exchange of old stock for a discounted amount of the new stock. This in effect reduces (maybe vastly) the wealth held by those who owned the original stock. Buying Stock in Company ABC Haniah buys stock in the ABC company, investing a total of $13,000. She expects the stock to grow, through stock price increase and reinvestment of dividends, by 12.3% per year and compounded annually. If she leaves that money invested, how much will the stocks be worth in 20 years? Calculating this is a compound interest calculation, if Haniah’s assumption about the stock’s performance is correct. If so, then the principal is $13,000, the rate is 0.123, the number of compounding periods per year is 1, and the time is 20 years. Substituting into the compound interest formula from Methods of Savings , and computing, we have A = P ( 1 + r n ) n t = $ 13,000 ( 1 + 0.123 1 ) 1 × 20 = $ 13,000 × 10.1764223996 = $ 132,293.49 . After 20 years, her stock is now worth $132,293.49. Risk and Volkswagen The question of risk hovers over every investment. How risky can it get? Volkswagen seems to be a rather safe investment. But in 2015, Volkswagen’s stock tumbled 30% over a few days when it was revealed that the company had installed software that altered the emission performance of some of their diesel engines. Volkswagen’s hope was that lower emissions would bolster US sales of some of their diesel models. This was a drastic drop, and many investors lost a lot of money. However, the stock has come back since then. This was mild compared to the 65% drop in the Martha Stewart Living Omnimedia stocks. Warren Buffett Warren Buffett is an investment legend. He began his career as an investment salesman in the 1950s. He formed Buffett associates in 1956. In 1965, he was in control of Berkshire Hathaway, which began as a merger between two textile companies. In his role there, he began to invest in a variety of companies. It is now a conglomerate holding company, and fully owns GEICO, Duracell, Diary Queen, and other large companies. His investment philosophy involves finding stocks and bonds from companies that have high intrinsic worth compared to their stock or bond prices. This means he focuses not on the supply and demand side of stock investing, but instead on the company’s worth in total. Using this philosophy, he has become one of the world’s most successful investors. Reading Stock Tables Information about particular stocks is contained in stock tables . This information includes how much the stock is selling for, and its high and low values form the past year (52 weeks). In a newspaper, the stock table may look like this: 52-Week High Low Stock SYM Div Yld % P/E Vol 100s High Low Close Net Chg 41.66 18.90 McDonald’s MCD .72 2.9 12 7588 25.73 23.87 25.42 +0.31 22.60 13.20 Monsanto MON .52 2.4 55 15474 21.86 21.48 21.64 -0.29 17.05 8.30 Motorola MOT .16 1.7 dd 16149 10.57 8.88 10.43 +0.14 31.75 22.99 Mueller MLI - - 16 1564 29.32 27.03 27.11 -0.02 excerpt from a stock table, 2008 The symbols and abbreviations are defined here: 52-week High 52-week Low The highest and lowest price of the stock over the past 52 weeks Stock SYM The name of the company and the symbol used for trading Annual DIV The current annual dividend per share Yld % Percent yield is = annual dividend share price × 100 P/E Price to earnings ratio, share price divided by earnings per share over past year (dd indicates loss) Vol 100s The number of shares traded yesterday in 100s High Low The highest and lowest prices at which stocks traded yesterday Close The price at which the stock traded at the close of the market yesterday Net Chg Net change; change in price from market close 2 days ago to yesterday’s close The formulas for yield and price to earnings is a good way to measure how much the stock returns per share. Their values are calculated in the stock table, but deserve attention here. The price to earnings ratio of a stock, P/E, is P / E = Share Price Dividend . The percent yield for a stock, Yld%, is Y l d % = Annual Dividend Share Price × 100 % . It should be noted that the price of a stock increases and decreases every moment, and so these value change as the share price changes. Computing Percent Yield Find the percent yield for a stock with a price of $30.69 and an annual dividend of $1.48. Find the percent yield for a stock with a price of $62.25 and an annual dividend of $1.76. Substituting the values for price, $30.69, and annual dividend, $1.48, we find the percent yield for the stock to be Y l d % = Annual Dividend Share Price × 100 % = $ 1.48 $ 30.69 × 100 % = 4.82 % Substituting the values for price, $62.25, and annual dividend, $1.76, we find the percent yield for the stock to be Yld% = Annual Dividend Share Price × 100 % = $ 1.76 $ 62.25 × 100 % = 2.83 % The stock table information is now, and has been, available online, from websites such as cnn.com/markets, markets.businessinsider.com/stocks, and marketwatch.com. The same information is available from these sites as from the newspaper listings, but are often accessed one stock at a time. shows the stock table for Lowe’s on September 7, 2022. Key data for Lowe's stock 9/7/2022 (data source: marketwatch.com) Other key data is further down on the website, and is shown in , below. Key data for Lowe's stock 9/7/2022 (data source: marketwatch.com) Notice that the 52-week high and low are now shown as the 52-week range. However, you get additional information, including the stock performance over the past 5 days, past month, past 3 months, the year to date (YTD), and over the past year. You can also read the number of shares outstanding, the expected date for the dividend (EX-DIVIDEND DATE), and importantly for the P/E ratio, the earning per share (EPS). Reading an Online Stock Table Consider the stock table ( ), and answer the questions based on the table. Key data for McDonald's stock 9/7/2022 (data source: marketwatch.com) What is the current price for McDonald’s Corp on this date? What is the 52-wk high? 52-wk low? When is the dividend expected? What is its yield? What is the earnings per share? Looking at the table, the current price of a share is $258.87. The high was $271.15, and the low was $217.68. August 31, 2022 2.13% The EPS value is $8.12. As mentioned, stocks earn money in two ways, through dividends and increase in share price. Dividends Paid Darma owns 150 shares of stock in the GDW company. This quarter, GDW is paying $0.87 per share in dividends. How much will Darma earn in dividends this quarter? Each share pays $0.87, so Darma earns 150 × $ 0.87 = $ 130.50 . Stock Price Increases Vincent buys 100 stocks in the REM company for $21.87 per share. One year later, he sells those 100 shares for $29.15 per share. How much money did Vincent make? What was his return on investment for that one year? Vincent spent $21.87 per share to buy the stock. The total he spent on the stock was $ 21.87 × 100 = $ 2,187.00 . When he sold the stock, the price was $29.15, so he received $ 29.15 × 100 = $ 2,915.00 . He made $ 2,915.00 - $ 2,187.00 = $ 728.00 . His return on investment was Earnings Original Price = $ 728 $ 2,187 = 33.29 % . Reading Stock Summary Online Mutual Funds A mutual fund is a collection of investments that are all bundled together. When you buy shares of a mutual fund, your money is pooled with the assets of other investors. This pooled money is invested in stocks, bonds, money market instruments, and other assets. Mutual funds are typically operated by professional money managers who allocate the fund's assets and attempt to produce capital gains or income for the fund's investors. A key benefit of mutual funds is that they allow small or individual investors to invest in professionally managed portfolios of equities, bonds, and other securities. This means each shareholder participates proportionally in the gains or losses of the fund. The performance of a mutual fund is usually stated as how much the mutual fund’s total value has increased or decreased. Since there are many different investments inside the mutual fund, the risk is reduced significantly, compared to direct ownership of stocks. Even so, mutual funds historically perform well and can earn more than 10% annually. The investments that make up a mutual fund are structured and maintained to match stated investment objectives, which are specified in its prospectus . A prospectus is a pamphlet or brochure that provides information about the mutual fund. Before buying shares of a mutual fund, consult its prospectus, consider its goals and strategies to see if they match your goals and values and also research any associated fees. Mutual Funds Investing in a Mutual Fund Kaitlyn has analyzed her $12,862.50 quarterly budget using the 50-30-20 budget philosophy, and sees she should be saving or paying down debt with $2,572.50 per quarter. She decides to invest $1,300 quarterly a mutual fund that reports an average return of 11.62% over the 18-year life of the mutual fund. Assuming that this interest rate continues, and is compounded quarterly, how much will her mutual fund account be worth after 5 years? Kaitlyn’s plan is an ordinary annuity, and so the future value of her account can be found using the formula F V = p m t × ( 1 + r / n ) n × t - 1 r / n , with a payment of $1,300, a rate of 0.1162, number of compounding periods 4, after 5 years. Substituting these values into the formula and calculating, we find F V = p m t × ( 1 + r / n ) n × t - 1 r / n = $ 1,300 × ( 1.02905 ) 20 - 1 0.02905 = $ 1,300 × 0.773084935178 0.032905 = $ 1,300 × 26.6122189784 = $ 34,595.88 Kaitlyn’s mutual fund will be worth $34,595.88 after 5 years. Investing in a Mutual Fund to Reach a Goal Kaitlyn wants to retire with $1,500,000 in her mutual fund account. She will invest for 35 years. The mutual fund reports an average return of 11.62% over the 18-year-long life of the mutual fund. Assuming that this interest rate continues, and is compounded quarterly, how much will she need to pay annually into her mutual fund to reach her goal? Kaitlyn’s plan is an ordinary annuity, and so the payment to reach her goal can be found using the formula p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1 , with a F V , or goal, of $1,500,000, a rate of 0.1162, for 35 years. Substituting these values into the formula and calculating, we find p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1 = $ 1,500,000 × ( 0.1162 / 1 ) ( 1 + 0.1162 / 1 ) 1 × 35 - 1 = $ 174,300 26.0558103113 = $ 6,689.49 Kaitlyn needs to invest $6,689.49 per year (or $557.46 per month) into the mutual fund to reach $1,500,000 in 35 years. Return on Investment As in Methods of Savings , the formula for return on investment is ROI = F V - P P . As indicated before, this formula does not take into account how long the investment took to reach its current value. It depends only on the initial value, P , and the value at the end of the investment, F V . Return on Investment for a Bond Recall , in which Muriel purchased a $3,000 bond with a maturity of 4 years at a fixed coupon rate of 5.5% paid annually. What was Muriel’s return on investment? Each year, Muriel received $165. She received this money four times, so earned a total of $660. This represents F V – P , or just the earnings. Using that we find that the ROI is ROI = 660 3000 = 0.22 , or 22%. As mentioned, the ROI does not address the length of time of the investment. A good way to do that is to equate the ROI to an account bearing interest that is compounded annually. The annual return is the average annual rate, or the annual percentage yield (APY) that would result in the same amount were the interest paid once a year. The formula for annual return is annual return = ( F V P ) ( 1 t ) - 1 , where t = the number of years, F V = new value, and P = starting principal. We apply this to the previous example. Annual Return on Investment for a Bond Recall , in which Muriel purchased a $3,000 bond with a maturity of 4 years at a fixed coupon rate of 5.5% paid annually. What was Muriel’s annual return on investment? Interpret this as compound interest. Muriel earned a total of $660. This represents F V – P , or just the earnings. The starting principal was $3,000. The value at the end of 4 years was $3,000 + $660 = $3,660. The time of the investment was 4 years. Using that we find that the annual return is annual return = ( F V P ) ( 1 t ) - 1 = ( $ 3,660 $ 3,000 ) ( 1 4 ) - 1 = 1.22 1 4 - 1 = 1.050969 = 0.050969 , or 5.10%. The 5.5% bond earned the equivalent of 5.10% compounded annually. In and Your Turn, the annual return was lower than the interest rate of the investment. This is because the interest from a bond is simple interest, but annual yield equates to compounded annually. Return on Investment for Stock in Company ABC Haniah buys stock in the ABC company, investing a total of $13,000. After 20 years, the stock is worth $132,293.49, including reinvestment of dividends. What is Haniah’s return on investment? What is Haniah’s annual return? To calculate Hanniah’s return on investment, substitute $13,000 for P and $132,293.49 for F V in the formula ROI = F V - P P and calculate. Doing so we find Haniah’s return on investment to be ROI = F V - P P = $ 132,293.49 - $ 13,000 $ 13,000 = 9.176422 , or 917.64% To calculate Haniah’s annual return, substitute $13,000 for P and $132,293.49 for F V in the formula annual return = ( F V P ) ( 1 t ) - 1 and calculate. Doing so we find her annual return to be annual return = ( F V P ) ( 1 t ) - 1 = ( $ 132,293.49 $ 13,000 ) ( 1 20 ) - 1 = 0.1230 , or 12.3% You should see that the annual return is equal to the annual compounded interest that was assumed for the stocks. Compute Payment to Reach a Financial Goal As in Methods of Savings , determining the payment necessary to reach a financial goal uses the payment formula for an ordinary annuity, p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1 . If dealing with mutual funds or stocks, an assumed annual interest rate, compounded, will be used. This value is often determined through research and informed speculation. Richard is saving for new siding for his home. He and his partner believe they will need $37,500 in 10 years to pay for the siding. How much should they invest yearly in a mutual fund they believe will have an annual interest rate of 12%, compounded annually, in order to reach their goal? The necessary annual payment is found using the function p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1 with F V = 37,500, r = 0.12, and n = 1. Substituting and calculating, we find the annual payment should be p m t = F V × ( r / n ) ( 1 + r / n ) n × t - 1 = $ 37,500 × ( 0.12 / 1 ) ( 1 + 0.12 / 1 ) 1 × 10 - 1 = $ 4,500 ( 1.12 ) 10 - 1 = $ 4,500 2.10584820834 = $ 2,136.91 Retirement Savings Plans We close this section by investigating the three main forms of retirement savings accounts: traditional individual retirement accounts (IRAs), Roth IRAs, and 401(k) accounts. Each has distinct characteristics that are suited to different investors’ needs. Individual Retirement Accounts A traditional IRA lets you contribute up to an amount set by the government, which may change from year to year. For example, the maximum contribution for 2022 is $6,000; $7,000 over age 50. Anyone is eligible to contribute to a traditional IRA, regardless of your income level. Your money grows tax-deferred, but withdrawals after age 59½ are taxed at current rates. Traditional IRAs also allow you to use the contribution itself as a deduction on a current year tax return. Roth IRAs allow contributions at the same levels as traditional IRAs, with a maximum $6,000 for 2022; $7,000 over age 50. However, to be eligible to make contributions, your earned income must be below a certain level. A Roth IRA allows after-tax contributions. In other words, the contribution itself is not tax-deductible, as it is with the traditional IRA. However, your money grows tax-free. If you make no withdrawals until you are age 59½, there are no penalties. IRAs pay a modest interest rate. In either case, IRA deposits have to be from earned income, which in effect means if your earned income is over $6,000 ($7,000) then you can deposit the maximum. Comparing Roth IRAs to Traditional IRAs Which type of IRA, Roth or traditional, has an income limit for its use? Roth IRAs require income to be below a certain limit. In 2022, the maximum that can be added to a Roth IRA was $6,000 for those under 50 years of age. For those over 50 years of age, the maximum that can be added to a Roth IRA is $7,000. However, to qualify for a Roth IRA in fall of 2022, a single person’s modified adjusted gross income (MAGI) must be below $129,000. Then, if a single person’s income is between $129,000 and $144,000, the maximum contribution is reduced from the limit for incomes below $129,000. For a married couples filing a joint tax return those values are $204,000 to $214,000. 401(k) Accounts Your employer may offer a retirement account to you. These are often in the form of a 401(k) account. There are traditional and Roth 401(k) accounts, which differ in how they are taxed, much as with other IRAs. In the traditional 401(k) plans, the money is deposited before tax is assessed, which means you do not pay taxes on this money. However, that means when money is withdrawn, it is taxed. These accounts are similar to mutual funds, in that the money is invested in a wide range of assets, spreading the risk. One of the perks some employers offer is to match some amount of your contributions to the 401(k) plan. For instance, they may match your deposits up to 5% of your income. This is an instant 100% return on the money that was matched. 401(k) Accounts Matching 401(k) Deposit Alice signs up for her employer-based 401(k). The employer matches any 401(k) contribution up to 6% of the employee salary. Alice’s annual salary is $51,600. What is the most money that Alice can deposit that will be fully matched by the company? How much total will be deposited into Alice’s account if she deposits the full 6%? How much return does Alice earn if she deposits exactly 6% in her 401(k)? The employer will match up to 6% of any employee’s salary. 6% of Alice’s salary is 0.06 × $ 51,600 = $ 3,096 . So Alice can deposit up to $3,096 and receive that amount in matching funds in her account. Alice’s contribution plus the company’s contribution is $ 3,096 + $ 3,096 = $ 6,192 , which is the total that is deposited into Alice’s account. She earns a 100% return on the day she deposits her $3,096. 401(k) plans with matching funds provide great value, as their rates of return are high compared to savings accounts, and are less risky that stocks since such funds invest across many investment vehicles. The next example demonstrates the power of constant deposits into a 401(k) plan that has some employer match. Constant Deposits into a 401(k) Plan DeJean begins depositing $300 per month from his paycheck each month in his employer-based 401(k) account. The employer matches this deposit as it falls below their matching threshold. DeJean expects the return to average 10% per year, compounded annually. How much will DeJean’s account be worth if he keeps making those payments for 30 years? What will his account be worth without the matching funds? This is a form of an ordinary annuity, so the formula F V = p m t × ( 1 + r / n ) n × t - 1 r / n will be used. The company matches DeJean’s full deposit, so each month $600 will be deposited. He is assuming the money will compound annually, so the amount deposited each year is needed as the value of pmt. For the year, he will deposit 12 × $ 600 = $ 7,200 . The rate is 0.1, the number of compounding periods is 1, and the number of years is 30. Substituting and calculating, the value of DeJean’s account after 30 years will be F V = p m t × ( 1 + r / n ) n × t - 1 r / n = $ 7,200 × ( 1 + 0.1 / 1 ) 1 × 30 - 1 0.1 / 1 = $ 7,200 × ( 1.1 ) 30 - 1 0.1 = $ 7,200 × 164.494022689 = $ 1,184,356.96 This is a form of an ordinary annuity, so the formula F V = p m t × ( 1 + r / n ) n × t - 1 r / n will be used but the deposit is now only $300 per month without the matching funds. For the year, he will deposit 12 × $ 300 = $ 3,600 . The rate is 0.1, the number of compounding periods is 1, and the number of years is 30. Substituting and calculating, the value of DeJean’s account after 30 years will be F V = p m t × ( 1 + r / n ) n × t - 1 r / n = $ 3,600 × ( 1 + 0.1 / 1 ) 1 × 30 - 1 0.1 / 1 = $ 3,600 × ( 1.1 ) 30 - 1 0.1 = $ 3,600 × 164.494022689 = $ 592,178.48 Check Your Understanding Key Terms Bonds Maturity date Stocks Dividend Mutual fund Prospectus Issue price Shares Stock table Individual retirement account Roth IRA 401(k) Key Concepts There are many different investments with different returns and risks. Bonds are loans form the purchaser to the entity selling the bond. Bonds have some tax benefits, low to no risk, and a low return. Stocks represent part ownership in a company. As such, stock holders share in the profits, and losses, of the company. Information, including price, P/E, yearly highs and lows, and dividend amount can be found in online stock tables available on many websites. Mutual funds represent collections of professionally administered investment vehicles. Have shares in a mutual fund has lower risk than ownership of stocks. Retirement accounts employ some of the same strategies as mutual funds, in that they spread the risk and are professionally managed. IRAs and Roth IRAs differ on when taxes are paid on the money, and who can use them. Roth IRAs have income limits while traditional IRAs do not. Videos Bonds Reading Stock Summary Online Mutual Funds 401(k) Accounts Formulas annual return = ( F V P ) ( 1 t ) - 1 P / E = Share Price Dividend Yld % = Annual Dividend Share Price × 100 %

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The Basics of Loans Loans are contracts that allow people to buy now but require them to pay more. (credit: "Closing" by Tim Pierce/Flickr, CC BY 2.0) Learning Objectives After completing this section, you should be able to: Describe various reasons for loans. Describe the terminology associated with loans. Understand how credit scoring works. Calculate the payment necessary to pay off a loan. Read an amortization table. Determine the cost to finance for a loan. New car envy is real. Some people look at a new car and feel that they too should have a new car. The search begins. They find the model they want, in the color they want, with the features they want, and then they look at the price. That’s often the point where the new car fever breaks and the reality of borrowing money to purchase the car enters the picture. This borrowing takes the form of a loan. In this section, we look at the basics of loans, including terminology, credit scores, payments, and the cost of borrowing money. Reasons for Loans Even if you want a new car because you need one, or if you need a new computer since your current one no longer runs as fast or smoothly as you would like, or you need a new chimney because the one on your house is crumbling, it’s likely you do not have that cost in cash. Those are very large purchases. How do you buy that if you don ’t have the cash? You borrow the money. And for helping you with your purchase, the company or bank charges you interest. Loans are taken out to pay for goods or services when a person does not have the cash to pay for the goods or services. We are most familiar with loans for the big purchases in our lives, such as cars, homes, and a college education. Loans are also taken out to pay for repairs, smaller purchases, and home goods like furniture and computers. Loans can come from a bank, or from the company selling the goods or providing the service. The borrower agrees to pay back more than the amount borrowed. So there is a cost to borrowing that should be considered when deciding on a purchase bought with credit or a borrowed money. Even using a credit card is a form of a loan. Essentially, a loan can be obtained for just about any purchase, large or small, that has a cost beyond a person’s cash on hand. The Terminology of Loans There are many words and acronyms that get used in relation to loans. A few are below. APR is the annual percentage rate. It is the annual interest paid on the money that was borrowed. The principal is the total amount of the loan, or that has been financed. A fixed interest rate loan has an interest rate that does not change during the life of the loan. A variable interest rate loan has an interest rate that may change during the life of the loan. The term of the loan is how long the borrower has to pay the loan back. An installment loan is a loan with a fixed period, and the borrower pays a fixed amount per period until the loan is paid off. The periods are almost uniformly monthly. Loan amortization is the process used to calculate how much of each payment will be applied to principal and how much is applied to interest. Revolving credit , also known as open-end credit, is how most credit cards work but is also a kind of loan account. (We will learn about credit cards in Credit Cards ) You can use up to some specified value, called the limit, any way you want, and as long as you pay the issuer of the credit according to their terms, you can keep borrowing from this account. These and other terminologies can be researched further at Forbes . Credit Scores Not everyone pays the same interest for the same loan. One person might get an APR of 2.9% while another pays 6.9%. These rates are based on your credit score. Data about you and your credit is collected by three credit bureaus—Experian, Equifax, and TransUnion. They calculate your score using one of two main models: FICO and Vantage Score. The score they develop is based on the following categories: Payment History: Making your payments on time and not missing payments is by far the most important factor. All three credit types—revolving, installment, and open—contribute to this factor. Credit Utilization or Amount Owed: How much do you owe on your credit card accounts? This category is concerned with the ratio of how much you owe on revolving credit accounts relative to your available credit, also known as your credit utilization ratio. This is the only category that depends solely on your revolving credit accounts. Length of Credit History: This is the average age of your credit history, including the age of the oldest and newest accounts. All three types of credit accounts play a role in this category. Credit Mix: This number represents the different types of credit accounts you have, such as credit cards, car loan, mortgages, and whether you are successful managing both revolving and installment accounts. New Credit: Have you recently opened a new account or applied for new credit? Lenders want to know how much new credit you are taking on. So, if you are planning to buy a car and make another large purchase with a credit card, you may want to space these purchases out. If you have done well in these categories, your credit score will be high, and you will qualify for lower interest rates because you are not perceived as being a risky investment. However, if you do poorly in these categories, your score will be low and you will pay higher interest rates since you present a greater risk. Check out this nerdwallet article on credit scores to learn more! Credit Scores Explained Where Do Interest Rates Come From? There are many factors that impact your interest rate beyond your credit score. Banks have the authority to set their own rates, so competition between banks impacts interest rates. Bank A doesn’t want to charge interest rates that are too high, since borrowers will find banks with better rates. Banks also don’t want to charge too little interest. The too little interest is more involved than the too high. The bank needs to make a profit on its loans. Deposits at the bank are used by the bank to generate loans. The bank has to pay those depositors interest. The bank must charge more for loans they give than they pay to people with deposits in the bank. Banks also borrow money from each other. These loans have an interest rate, and once more, the bank making a loan must make a profit. More directly, they must charge more for loans they give than they pay for loans they take. In the United States, banks may also borrow from the Federal Reserve, which also charges an interest rate, which is also called the discount rate. This is where a bank’s prime rate comes from. A bank’s prime rate is the interest rate it will give to its very best customers, which means most customers will pay more than the bank’s prime rate. To confuse the issue, there is also the Wall Street Journal ’s prime rate. It is the average of the prime rates charged by individual banks. The Wall Street Journal surveys several banks to generate this value. Banks also increase the interest rate charged to customers based on both the credit risk presented by the customer, and the risk associate with what the loan will be used for. Calculating Loan Payments Loan payments are made up of two components. One component is the interest that accrued during the payment period. The other component is part of the principal. This should remind you of partial payments from Simple Interest . Over the course of the loan, the amount of principal remaining to be paid decreases. The interest you pay in a month is based on the remaining principal, just as in the partial payments of Simple Interest . The amount of interest, I , to be paid for one period of a loan with remaining principal P is I = P × r n , where r is the interest rate in decimal form and n is he number of payments in a year (most often n = 12). Since the interest is for the one period, the time is 1 and does not impact the calculation. Note, interest paid to lenders is always rounded up to the next penny. Interest for a Monthly Payment of a Loan Find the interest to be paid for the period on loans with the following remaining principal and given annual interest rate. Each period is a month. Remaining principal is $13,450, interest rate is 6.75% Remaining principal is $8,460, interest rate is 5.99% Substituting $13,450 for the remaining principal P , 0.0675 for r , and n = 12 since the period is a month into the formula, we find that the interest to be paid this period is I = P × r n = $ 13 , 450 × 0.0675 12 = $ 75.66 . Substituting $8,460 for the remaining principal P , 0.0599 for r , and n = 12 since the period is a month into the formula, we find that the interest to be paid this period is I = P × r n = $ 8 , 450 × 0.0599 12 = $ 42.18 . The payment of the loan has to be such that the principal of the loan is paid off with the last payment. In any period, the amount of interest is defined by the formula above, but changes from period to period since the principal is decreasing with each payment. The trick is knowing how much principal should be paid each payment so that the loan is paid off at the stated time. Fortunately, that is found using the following formula. The payment, pmt , per period to pay down a loan with beginning principal P is p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 , where r is the annual interest rate in decimal form, t is the number of years of the loan, and n is the number of payments per year (typically, loans are paid monthly making n = 12). Note, payment to lenders is always rounded up to the next penny. Often, the formula takes the form p m t = P × ( r ) × ( 1 + r ) n ( 1 + r ) n − 1 , where r is the interest rate per period (annual rate divided by the number of periods per year), and n is the total number of payments to be made. Calculating the Payment for a Loan In the following, calculate the payment necessary to pay off the loan with the given details. The payments are monthly. A car loan taken out for $28,500 at an annual interest rate of 3.99% for 5 years. A home loan taken out for $136,700 and an annual interest rate of 5.75% for 15 years. The loan is for $28,500, which is the principal. The rate is 3.99%, so r = 0.0399. The term of the loan is 5 years, so t =5. Monthly payments means n = 12. Substituting these values for P , r , n , and t into the formula p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 and calculating, we find the payment for the loan. p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 28 , 500 × ( 0.0399 / 12 ) × ( 1 + 0.399 / 12 ) 12 × 5 ( 1 + 0.0399 / 12 ) 12 × 5 − 1 = $ 28 , 500 × ( 0.003325 ) × ( 1.003325 ) 60 ( 1.003325 ) 60 − 1 = $ 115.6470437 0.220388273 = $ 524.75 The monthly payment needed is $524.75. The loan is for $136,000, which is the principal P . The rate is 5.75% so r = 0.0575. The term of the loan is 15 years, so n = 15. Monthly payments mean n =12. Substituting these values for P , r , n , and t into the formula p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 and calculating, we find the payment for the loan. p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 136 , 700 × ( 0.0575 / 12 ) × ( 1 + 0.0575 / 12 ) 12 × 15 ( 1 + 0.0575 / 12 ) 12 × 15 − 1 = $ 28 , 500 × ( 0.0047917 ) × ( 1.0047917 ) 180 ( 1.003325 ) 180 − 1 = $ 1 , 548.600986 1.364201118 = $ 1,135.18 The monthly payment needed is $1,135.18. Using Google Sheets to Calculate Loan Payments Google Sheets has a formula to calculate the monthly payment necessary to pay off a loan with a specified interest rate and term. The formula is the PMT formula. It uses the principal P , interest rate r , and t years. Follow these steps Open a Google worksheet and click on any cell. Type =-PMT(r/12,12*t,P). Hit the enter key. The cell displays the payment. Please note the negative sign. Since Google Sheets is a spreadsheet program, is sees the payment as funds leaving the account, and so they are, by default, negative. The negative sign in front of the formula makes the result positive. For example, for a $50,000 loan at 10.9% interest for 7 years, you would type =-PMT(0.109/12,12*7,50000). The formula and the result are shown in . Google Sheets formula Alternatively, you can also use an online calculator to find monthly payments for a loan, such as the one at Caluculator.net Reading Amortization Tables An amortization table or amortization schedule is a table that provides the details of the periodic payments for a loan where the payments are applied to both the principal and the interest. The principal of the loan is paid down over the life of the loan. Typically, the payments each period are equal. Importantly, one of the columns will show how much of each payment is used for interest, another column shows how much is applied to the outstanding principal, and another column shows the remaining principal or balance . Amortization table Reading from an Amortization Table Using the partial amortization table (Figure 6.23) , answer the following questions. Amortization table What is the loan amount (principal), the interest rate, and the term of the loan? How much is the monthly payment? How much remaining balance is there after the payment in month 15? How much was the interest in payment 10? What is the total of the interest paid after payment 18? What happens to the amount paid in interest each month? Reading the values at the top of the table, we see the principal is $10,000, the interest rate is 4.75%, and has a term of 20 years. The monthly payment is listed below the term of the loan, and is $64.62. $9,613.83 $38.68 $697.01 The amount paid to interest decreases each month. Reading an Amortization Table Cost of Finance There are often costs associated with a loan beyond the interest being paid. The cost of finance of a loan is the sum of all costs, fees, interest, and other charges paid over the life of the loan. Cost of Financing a Personal Loan Irena signed for a loan of $15,000 at 6.33% for 5 years. When she took out the loan, Irena paid a $750 origination fee. Over the course of the loan, she pays $2,537.96 in interest. What was her cost to finance the loan? The cost of finance is the sum is all interest and any fees paid for the loan. The fees paid were $750.00 and the interest was $2,537.96. Her cost of finance for this loan was $3,287.96. Check Your Understanding Key Terms Fixed interest rate Variable interest rate Installment loan Loan amortization Revolving credit Amortization table Cost of finance Key Concepts There are many reasons for a loan, but primarily it is taken out for a large expense when cash is not available. Each payment for an installment loan consists of an interest portion and a principal portion. There is a formula to calculate the payment necessary to pay off a loan in installments. Amortization schedules, or tables, show how each payment is applied to principal and interest. It also includes other details such as remaining balance and total interest paid. Loans often have other fees associated with them such as origination fees or application fees. The total of the interest paid and the fees is the cost of finance. Video Credit Scores Explained Reading an Amortization Table Formula I = P × r n p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1

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Understanding Student Loans College is often paid for through loans. (credit: "Sidewalk Scene in front of Science Building" by IMCBerea College Wikimedia Commons, CC- BY 2.0) Learning Objectives After completing this section, you should be able to: Describe how to obtain a student loan. Distinguish between federal and private student loans and state distinctions. Understand the limits on student loans. Summarize the standard prepayment plan. Understand student loan consolidation. Summarize and describe benefits or drawbacks of other repayment plans. Summarize possible courses of action if a student loan defaults. Obtaining a Student Loan All college students are eligible to apply for a loan regardless of their financial situation or credit rating. Federal student loans do not require a co-signer or a credit check. Most students do not have a credit history when they begin college, and the federal government is aware of this. However, private loans will generally require a co-signer as well as a credit check. The co-signer will assume responsibility for paying off the loan if the student cannot make the payments. The first step in applying for student loans is to fill out the FAFSA (Free Application for Student Aid). FAFSA determines financial need and what type of loan the student is qualified to obtain. For students who are still dependents on their parent’s taxes, the parents also fill out the FAFSA, as their wealth and income impacts what the dependent student is eligible for. Students who cannot demonstrate financial need will also be helped by applying with FAFSA, as it will help guide them to the type of loan most appropriate. The FAFSA must be submitted each year. The FAFSA deadline is the spring of the student’s next academic year. The deadline is often in March. Do not allow this deadline to pass. As soon as an offer letter from the college is received, the student should start the application process. The college will determine the loan amount needed. Also, there are limits on the amount a student can borrow. There are both yearly limits and aggregate limits. See the table later in this section that outlines the loan limits per school year and in the aggregate. If the student receives a direct subsidized loan, there is a limit on the eligibility period. The time limit on eligibility depends on the college program into which the student enrolls. The school publishes how long a program is expected to take. The eligibility period is 150% of that published time. For example, if a student is enrolled in a 4-year program, such as a bachelor’s degree program, their eligibility period is 6 years, as 1.50(4) = 6. Therefore, the student may receive direct subsidized loans for a period of 6 years. Types and Features of Student Loans Once a tuition statement is received, and all the non-loan awards are analyzed that are applicable to the costs of college (such as scholarships and grants), there still may be quite of bit of an expense to attend college. This difference between what college will cost (including tuition, room and board, books, computers) and the non-loan awards received is the college funding gap. College Funding Gap Ishraq receives her award and tuition letter from the college she wants to attend. Her tuition, fees, books, and room and board all come to $24,845 for the year. Her non-loan awards include an instant scholarship from the school for $7,500, a scholarship she earned for enrolling in a STEM program for $3,750, and a $1,000 scholarship from her church. What is Ishraq’s college funding gap? Her awards total to $12,250. Her cost to attend is $24,845. Her college funding gap is then $ 24,845 − $ 12,250 = $ 12,595 . She will need to find $12,595 in funding. There are several loan types, which basically break down into four broad categories: subsidized loans, unsubsidized loans, PLUS loans, and private loans. These loans are meant to fill the college funding gap. Federal subsidized loans are backed by the U.S. Department of Education. These loans are intended for undergraduate students who can demonstrate financial need. Subsidized federal loans, including Stafford loans, defer payments until the student has graduated. During the deferment, the government pays the interest while the student is enrolled at least half-time. These loans are generally made directly to students. However, there are restrictions on how the money can be used. It can only be used for tuition, room and board, computers, books, fees, and college-related expenses. Interest rates are not based on the financial markets but determined by Congress. Federal loans are backed by the Department of Education. Federal unsubsidized loans , including unsubsidized Stafford loans, are available for undergraduate and graduate students who cannot demonstrate financial need. If the student meets the program requirements, they are automatically approved. The student is not required to pay these loans during their time in college (enrolled at least half-time). However, the interest rate is generally higher and there is no deferment period, as with subsidized loans. Interest begins accruing as soon as the money is disbursed. The immediate accrual of interest means the balance of the loan grows as the student attends school. A loan that was for $10,000 can grow past $13,000 over five years of college. Some advisors tell students to pay the interest portion of the loan while it is deferred to prevent this growth of debt. Parent Loans for Undergraduate Students (PLUS) are federal loans made directly to parents. They are available even if parents are not deemed financially needy. A credit check is performed and approval is not automatic. The limit to what parents can borrow from a PLUS loan each year is still the college funding gap, but the aggregate of the PLUS loans does not have a limit. This means the PLUS loan can cover whatever is left in the funding gap once all other aid and loans are applied. Payments do not begin until the student is out of school, but interest begins to accrue the moment funds are disbursed. Because the parents take out the loan, the parents are responsible for paying back the loan. Private student loans are backed by a bank or credit institution and require a credit check, and interest rates are variable. As private loans are not subsidized by the government, no one pays the interest but the borrower. The student does not have to start repaying the loan until after graduation, but interest starts to accrue immediately. This loan has fewer repayment options, more fees and penalties, and the loan cannot be discharged through bankruptcy. Many students need a co-signer to acquire a private loan. Like PLUS loans, private student loans can cover whatever is left in the funding gap once all other aid and loans are applied Student loans, in general, have a term of 10 years, that is, the loans are paid back over 10 years. This can vary, but 10 years is the standard. School-Channel Loans and Direct-to-Consumer Loans Private loans can fall into one of two categories: school-channel loans and direct to consumer loans. School-channel loans are disbursed directly to the school. The school verifies the loan does not exceed the cost to attend school. Direct–to-consumer loans do not have the verification process. Those proceeds are sent directly to the borrower. They are processed more quickly, but often have higher interest rates. Types of Student Loans Limits on Student Loans As mentioned earlier, there are limits to how much a student can borrow, per year and in total. The following table shows a general breakdown of the amounts the federal government and private lenders will lend. Amounts are based on level of need and whether the student is a dependent or an independent student. Independent students include those who are at least 24 years old, married, a professional, a graduate student, a veteran, a member of the armed forces, an emancipated minor, or an orphan. The amounts shown are as of this writing in 2022. Year Dependent Students Maximum Amounts Independent Students Maximum Amounts First-Year Undergraduate $5,500 but no more than $3,500 may be in subsidized loans $9,500 but no more than $3,500 may be in subsidized loans Second-Year Undergraduate $6,500 but no more than $4,500 may be subsidized loans $10,500 but no more than $4,500 in subsidized loans Third Year and Additional Years $7,500 but no more than $5,500 may be in subsidized loans $12,500 but no more than $5,500 may be in subsidized loans Graduate and Professional Not applicable $20,500 in unsubsidized loans Limits $31,000 but no more than $23,000 in subsidized loans $57,500 for undergraduates but no more than $23,000 in subsidized. $138,500 for graduate or professional but no more than $65,500 may be subsidized loans. Check out this Edvisors page on the limits of student borrowing to learn more! Loan for Year 5 of College Efraim is a dependent undergraduate student enrolled in a biology program. He’s about to attend for the fifth year. In year 1 he took out $5,000 in federal subsidized and unsubsidized loans, in year 2 he took out $6,400 in federal subsidized and unsubsidized loans, in years 3 and 4, he took out the maximum federal subsidized and unsubsidized loans amounts. He needs federal subsidized and unsubsidized loans for his fifth year of school. How much can he obtain in federal subsidized and unsubsidized student loans? The sum of his previous loans is $ 5,000 + $ 6,400 + $ 7,500 + $ 7,500 = $ 26,400 . The limit for federal subsidized and unsubsidized loans is $31,000, so in year 5 he can get student loans in the amount of $ 31,000 − $ 26,400 = $ 4,600 . Putting this all together, we have a way to determine the student loans needed for a student to attend college. First, determine the funding gap. If the student or family can cover the gap, then no loans are necessary. Second, determine how much in federal subsidized and unsubsidized student loans can be taken out. If the total federal loans available is more than the funding gap, no other loans are needed. Third, if the federal subsidized and unsubsidized loans do not cover the gap, PLUS and private student loans can be taken out to cover the remainder of the gap. At each step, if the student and family can cover some or all of the gap, they can do so without taking out a loan. College Funding Gap and PLUS and Private Student Loans Olivia receives her award and tuition letter from the college she wants to attend. Her tuition, fees, books, and room and board all come to $44,845 for her second year. Her non-loan awards include an instant scholarship from the school for $13,500, a scholarship she earned for enrolling in an engineering program for $5,750, and a $2,000 scholarship from her parent’s workplace. For her first year, what is Olivia’s college funding gap? How much can Olivia borrow in federal subsidized and unsubsidized student loans? Once Olivia takes out her maximum subsidized and unsubsidized federal student loans, how much will have to be paid for using PLUS and private student loans? Her awards total to $21,250. Her cost to attend is $44,845. Her college funding gap is then $ 44,845 − $ 21,250 = $ 23,595 . The maximum in federal student loans that Olivia can borrow is $6,500 in year 2. The remaining funding gap is $ 23,595 − $ 6,500 = $ 17,095 . Private student loans, PLUS loans, or other sources must be used to cover this gap. Student Loan Interest Rates Student loans are first and foremost loans. Students will pay them back and will pay interest. In the fall of 2022, the federal student loan interest rate was 4.99%. Private student loans rates ranged between 3.22% and 13.95%. Finding the lowest interest rate you can helps with the payments, and especially helps if the loan is not federally subsidized. Remember, if the loan is not federally subsidized, the student is on the hook for the interest that is accumulating with the loan. Interest Accrual The interest on student loans begins as soon as the loan is disbursed (paid to the borrower). When the loan is federally subsidized, the government pays that interest for the student. This means the loan for a subsidized loan of $3,000 is still a loan for $3,000 when the student graduates. However, if the loan is not federally subsidized, the student is responsible for the interest that accrues on the loan. The $3,000 loan from year 1 of college is now a loan for more due to that added interest. The interest on that loan grew while the student was in college. The formula for growth of the loan’s balance is the same as compound interest formula from Compound Interest , A = P ( 1 + r n ) n t . Denise takes out unsubsidized student loan, in August, in her first year of college for $2,000. She manages an interest rate of 8%. She graduates after her fifth year of college, in May. She does not pay the interest on the loan during her time in college. What is the balance of her first year loan in May of her graduation year? The principal of the loan is $2,000. Her interest rate is 8%. Since student loans are typically paid monthly, there are 12 periods per year. Since the time she has had the loan is not in years, we will use the number of months for the value of nt in the formula. She has had the loan for 4 years and 9 months, meaning 57 period have passed. Substituting those values into the formula and calculating, we find her balance in May of her graduating year is A = P ( 1 + r n ) n t = $ 2,000 ( 1 + 0.08 12 ) 57 = $ 2,000 ( 1.0 6 ¯ ) 57 = $ 2,920.89 . The Standard Repayment Plan There are various repayment plans available. The one most likely to apply to a student loan is the standard repayment plan, which is available to everyone. Borrowers pay a fixed amount monthly so the loan is paid in full within 10 years. Consolidated loans, discussed later in this section, also qualify for the standard repayment plan, and may allow the payoff period to range from 10 to 30 years. Direct subsidized and unsubsidized loans, PLUS loans, and federal Stafford loans are eligible. Since these are loans, they are paid back with interest. As with most installment loans, their payments are due monthly. The formula for paying back these loans is the same as the formula used for paying loans in The Basics of Loans : p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 . Using that formula, we can calculate how much the payment is for a student loan. Remember that all loan payments are rounded up to the next penny. Standard Repayment Plan Find the payment for the following student loans using the standard repayment plan: Loan is $3,500, interest is 4.99% Loan is for $6,200, interest is 6.75% The principal is P = $3,500 and the rate is r = 0.0499. Since this is the standard repayment plan, there are n = 12 payments per year for 10 years. Substituting those values into p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 and calculating gives a monthly payment of p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 3,500 × ( 0.0499 / 12 ) × ( 1 + 0.0499 / 12 ) 12 × 10 ( 1 + 0.0499 / 12 ) 12 × 10 − 1 = $ 3,500 × ( 0.004158 3 ¯ ) × ( 1.004158 3 ¯ ) 120 ( 1.004158 3 ¯ ) 120 − 1 = $ 23.9469911276 0.645370131872 = $ 37.11 The principal is P = $6,200 and the rate is r = 0.0675. Since this is the standard repayment plan, there are n = 12 payments per year for 10 years. Substituting those values into p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 and calculating gives a monthly payment of p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 6,200 × ( 0.0675 / 12 ) × ( 1 + 0.0675 / 12 ) 12 × 10 ( 1 + 0.0675 / 12 ) 12 × 10 − 1 = $ 6,200 × ( 0.005625 ) × ( 1.005625 ) 120 ( 1.005625 ) 120 − 1 = 68.3662233426 0.960321816275 = $ 71.20 Standard Repayment Plan for an Unsubsidized Loan Erson has a balance of $8,132.55 when he starts paying off the 8.6% unsubsidized student loan he took out in his third year. How much are his payments if the term for his loan is the standard 10 years? Using the payment formula, p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 , with P = $8,132.55, r = 0.086, t = 10 and n = 12, we calculate that his monthly payment will be p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 8,132.55 × ( 0.086 / 12 ) × ( 1 + 0.086 / 12 ) 12 × 10 ( 1 + 0.086 / 12 ) 12 × 10 − 1 = $ 8,132.55 × ( 0.0071 6 ¯ ) × ( 1.0071 6 ¯ ) 120 ( 1.0071 6 ¯ ) 120 − 1 = 137.310962384 1.35592393158 = $ 101.27 Student Loan Consolidation When a student graduates, they may have multiple different student loans. Keeping track of them and paying them off separately can be a burden. Instead, these loans can be consolidated into a single loan. If they are federal loans the combination is called federal consolidation. Combining private loans is often referred to as refinancing. Refinancing, or private consolidation, can be used to combine both private and federal student loans. Be aware that consolidated federal loans may still be subject to the rules and protections that govern subsidized loans. Refinancing loans, private or federal, are no longer subject to those rules and guidelines. Check out this Experian article about consolidation and refinancing for more deatil. In consolidation of federal direct student loans, the interest rate is the weighted average of the interest rates on the subsidized loans. This means the interest rate remains the same. However, if the term is extended, then the student will pay back more over time than if they did not extend the loan term. In refinancing, it is possible to obtain a lower interest rate on the student loans, which may lower how much is paid per month and lower the total paid back over time. These monthly payments are calculated using the same formula as for any other loan payment, p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 . The term of the refinanced loan may also be changed, which would also impact the payment per month. In either case, consolidating or refinancing, the monthly financial burden on the student can decrease. However, if the term is extended, the total amount repaid may increase. Federal Loan Consolidation and Interest Rates Ernest has four federal student loans that he wants to consolidate. He combines them into one loan. What is the maximum Ernest can reduce the interest rate by? Consolidating subsidized loans has no impact on the interest rate of the loans, so the maximum that the interest rate can be reduced is 0%. Payments for Consolidated Student Loans Brianna consolidates her student loans, some federal and some private, into a single refinanced student loan with a principal of $27,800. The interest rate that Brianna received was 8.375%. If Brianna’s new term is 15 years, how much are her payments per month? The principal is P = $27,800 and the rate is r = 0.08375. Since the payments are monthly, n =12. The loan term is for 15 years, so t = 15. years. Substituting those values into p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 and calculating gives a monthly payment of p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 = $ 27,800 × ( 0.08375 / 12 ) × ( 1 + 0.08375 / 12 ) 12 × 15 ( 1 + 0.08375 / 12 ) 12 × 15 − 1 = $ 6,200 × ( 0.0069791 6 ¯ ) × ( 1.0069791 6 ¯ ) 180 ( 1.0069791 6 ¯ ) 180 − 1 = $ 678.477992464 2.49693370968 = $ 271.73 Other Repayment Plans There are various other repayment plans available to students. Plans other than the standard repayment plan typically require the student to meet certain criteria. The following plans are independent of student income, but may make early payments easier. Graduated repayment plans are plans where the amount of payments gradually increases so that the loan is paid off in 10 years, or within 10 to 30 years for consolidated loans. Payments start off small and increase approximately every 2 years. Almost all loan types are eligible, including direct subsidized and unsubsidized loans, Stafford loans, PLUS loans, and consolidated loans. Extended repayment plans are available to the direct loan borrower if the outstanding direct loans are over $30,000. The payments, fixed or graduated, are designed so that the loans are satisfied within 25 years. Eligible loans include both direct subsidized or unsubsidized loans, Stafford loans, PLUS loans, and consolidated loans. If student earnings are such that the standard, graduated, or extended repayment plans are unaffordable, then one can make payments that are based on their discretionary income. Discretionary income is federally defined to be the difference between (adjusted) gross income and 150% of the poverty guideline for location and family size. This discretionary income then depends on where one lives (contiguous United States or Hawaii or Alaska) and how many dependents one has. If married, a spouse’s income will be included in the adjusted gross income. Understanding discretionary income is necessary to understand how income driven payments plans work. Discretionary Income The poverty guideline for a single person living in Arkansas, is $12,000. If Harriet is a single person in Arkansas with a (adjusted) gross income of $23,500, what is her discretionary income? For California, the poverty guideline for a person with four people in the household is $27,750. If such a person has a (adjusted) gross income of $48,600, what is their discretionary income? The poverty guideline for a single person in Arkansas is $12,000. 150% of that guideline value is 1.5 × $ 12,000 = $ 18,000 . The gross income that Harriet makes over that $18,000 is her discretionary income. That gross income is $23,500, so her discretionary income is $ 23,500 - $ 18,000 = $ 5,500 . The poverty guideline for a household of four in California is $27,750. 150% of that guideline value is 1.5 × $ 27,750 = $ 41,625 . The gross income that Harriet makes over that $41,625 is her discretionary income. That gross income is $48,600, so her discretionary income is $ 48,600 − $ 41,625 = $ 6,975 . The following plans all depend on discretionary income. Pay As You Earn (PAYE) repayment plans have monthly payments that are 10% of discretionary income based on a student’s updated income and family size. If a borrower files a joint tax return, their spouse’s income and debt may also be considered. Eligible loans include direct subsidized and unsubsidized loans, PLUS loans made to students, and some consolidated loans. These loans are forgiven (student does not pay the remaining balance) after 20 years of monthly payments if they were direct federal student loans. Revised Pay As You Earn (REPAYE) repayment plans have payment amounts that are based on income and family size and calculated as 10% of discretionary income. Eligible loans include direct subsidized and unsubsidized loans, direct PLUS loans, and some consolidated loans. These loans are forgiven, that is, the student does not pay more, after 20 or 25 years, provided they were direct federal student loans. Income-Based Repayment (IBR) plans sound like a few of the others and there are similarities in all of them. The payments are either 10% or 15% of discretionary income, but this plan is meant for those with a relatively high debt. Every year, income and family size must be updated, and payments are calculated based on those figures. Eligible loans include direct subsidized and unsubsidized loans, Stafford loans, and PLUS loans made to students, but not PLUS loans made to parents. Income-Contingent Repayment (ICR) plans have payments that are either 20% of discretionary income or whatever would be paid if a student were on a fixed payment plan for more than 12 years, whichever is less. Eligible loans include direct subsidized and unsubsidized, PLUS loans to students, and consolidated loans. There are many similarities among these repayment plans, and it is easy to misunderstand the nuances of each. Therefore, be careful entering into any type of repayment contract until you fully understand all the details and repercussions of the plan you choose. For more detail, see this nerdwallet article "Income-Driven Repayment: Is It Right for You?" to learn more ! Payments for a REPAYE Program Warren qualifies for a REPAYE payment plan. His gross income is $32,700. He is single and live in Montana, so the federal poverty guideline for Warren is $12,000. What is Warren’s discretionary income? Under the REPAYE plan, he pays 10% of his discretionary income, but monthly. How much are Warren’s REPAYE payments? The poverty guideline for Warren is $12,000. 150% of that guideline value is 1.5 * $ 12,000 = $ 18,000 . The gross income that Warren makes over that $18,000 is his discretionary income. That gross income is $32,700, so his discretionary income is $ 32,700 − $ 18,000 = $ 14,700 . 10% of Warren’s discretionary income is 0.1 × $ 14,700 = $ 1,470 . He pays monthly, so his monthly payments are $1,470 divided by 12, or $122.50 per month. Using income to determine payments initially seems excellent. However, if there is no forgiveness at the end of the loan, then the income driven payment plans can cause problems. For one, your payment may not be sufficient to cover the interest rate of your loans. In that case, your loan balance actually increases as you make your payments. Eventually, you are paying for not only your original loan balance, but interest that has been growing and compounding over time. Also, if the loan term is extended, you may pay more, perhaps a lot more, money over time. You may find yourself in the position of paying these loans for decades. With those possible drawbacks, great care must be taken to avoid large problems down the line. Repayment Plans Student Loan Default and Consequences The first day a payment is late, the account becomes delinquent . After 90 days, this delinquency is reported to the credit bureaus, and goes into default . This is serious, as now a credit score is affected, meaning that it will be harder to buy a car, a home, get a credit card, or a cell phone. Even renting an apartment may be a task not easily overcome. The default rate for students who do not complete their degree is three times higher than for students who do. Further, defaulting on a student loan may mean that the borrower loses eligibility for repayment plans, as the balance and any unpaid interest may become due immediately, and any tax refunds may be withheld and applied to the loan, and wages may be garnished. One should immediately contact your loan servicer and try to make other arrangements for repayment if this situation becomes apparent, as different repayment plans are available, if actions are taken quickly. There are several options that may be open to avoid defaulting. One is called rehabilitation, or is the process in which a borrower may bring a student loan out of default by adhering to specified repayment requirements, and the other is consolidation. Certain criteria must be met to enter these programs. Both of these options are detailed, including the criteria required for eligibility, on the studentaid.gov loan management page . Professionals advise hiring an attorney if one of these paths is chosen. Check Your Understanding Key Terms FAFSA College funding gap Subsidized loan Unsubsidized loan Parent loan for undergraduate students Private student loan School-channel loan Direct-to-consumer loan Standard repayment plan Federal consolidation Refinancing Private consolidation Graduated repayment plan Extended repayment plan Discretionary income Pay as you earn (PAYE) repayment plan Revised pay as you earn (REPAYE) repayment plan Income-based (IBR) repayment plan Income-contingent (ICR) repayment plan Delinquent Default Rehabilitation Key Concepts The FAFSA must be filled out each year that a student wishes to borrow for. A student’s funding gap determines how much they need in loans to pay for college. Federal subsidized student loans defer payments until after graduation and interest does not accrue on these loans. Unsubsidized student loans defer payment until after graduation but interest begins accruing as soon as the loan finds are disbursed. There are both yearly and aggregate limits for student loans to prevent over-borrowing, among other reasons. Federal direct loans have a low interest rate set by the government, but other student loans have varying rates of interest set by the banks. The standard repayment plan lasts 10 years and is made up of monthly payments. Consolidating or refinancing student loans merges many student loans into one loan. If only federal loans are consolidated, the interest rate is the same as the individual loans, currently set at 4.99%. If other loans are refinanced together, the interest rate may be lower with the new loan. Other repayment plans are available. Such a plan may have payment that start small and grow as the loan is paid off, or it may have a longer term, or may be based on the discretionary income of the student. Being delinquent on a student loan is a precursor to being in default. Making payments in a timely fashion allows the student to avoid this situation. Video Types of Student Loans Repayment Plans Formula funding gap = total cost − all aid A = P ( 1 + r n ) n t p m t = P × ( r / n ) × ( 1 + r / n ) n × t ( 1 + r / n ) n × t − 1 discretionary income = gross income − 1.5 × poverty guideline

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