Chapter 8.4, Problem 68E

Use the result of Problem 66 to show that if the minimum monthly payments are always calculated the same way and the borrower never pays more than the minimum that the loan will technically never reach a zero balance. Then explain why that doesn’t mean that realistically it won’t ever be paid off.

66. Here’s another approach to the calculation in Example 8. It’s actually like a savings account with negative interest: instead of 1% of the amount being added each compounding period (month in this case), 1% is being subtracted from the amount. Use the compound interest formula with a principal balance of $2,300 and interest of −1% per month compounded monthly for 6 months. How does the result compare to the calculations in Example 8?

EXAMPLE 8 Studying the Effect of Making Minimum Payments

Suppose you have a $2,300 balance on a credit card with an interest rate of 1.1% per month, and the minimum payment for any month is the amount of interest plus 1% of the principal balance. If you don’t make any more purchases on that card and make the minimum payment for 6 months, how much will you pay down the balance?