Problem        “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 first five years before the payment is due.  You feel comfortable with setting 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 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 of d = 275, r = 0.05 (annual rate), and n = 60, and the savings formula with r replaced by r/12 (the monthly interest rate).  You will find that the amount accumulated is not enough.  Change r to 0.09, it’s more than enough.  Try other values until you determine r to two decimal places.”

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                                                                    Problem

 

     “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 first five years before the payment is due.  You feel comfortable with setting 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 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 of d = 275, r = 0.05 (annual rate), and n = 60, and the savings formula with r replaced by r/12 (the monthly interest rate).  You will find that the amount accumulated is not enough.  Change r to 0.09, it’s more than enough.  Try other values until you determine r to two decimal places.”

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