Refer to the following in doing Exercises 73–75. In the savings formula, the interest rate appears twice. The particular ways in which is involved make it impossible to solve it algebraically to get an explicit formula for . However, with the help of a spreadsheet, you can find approximately when the other quantities are given.
75. (Spreadsheet helpful) Suppose that your parents are willing to lend you $20,000 for part of the cost of your college education and living expenses. They want you to repay them the $20,000, without any interest, in a lump sum 15 years after you graduate, when they plan to retire and move. Meanwhile, you will be busy repaying federally guaranteed loans for the first 10 years after graduation. But you realize that you won’t be able to repay the lump sum without saving up. So you decide that you will put aside money in an interest-bearing account every month for the five years before the payment is due. You feel comfortable with putting aside $275 a month (the amount of the payment on your college loans, which will be paid off after 10 years).
How high an annual nominal interest rate on savings do you need to accumulate the $20,000 in 60 months, if interest is compounded monthly? Enter into a spreadsheet the values (annual rate), and , and the savings formula with replaced by (the monthly interest rate). You will find that the amount accumulated is not enough. Change to 0.09; it’s more than enough. Try other values until you determine to two decimal places.
75.
0.634% per month, or 7.61% annual rate; you can get the same result in a spreadsheet with = 12* RATE(60, −275,0,20000,0,0.05/12). Since there is no exact formula for the interest rate, the spreadsheet uses a similar but more efficient method of successive approximation.