Exercise 31

Refer to the following for Exercises 31-35, about credit card payments. Many credit cards use a similar formula for the minimum payment, which is the new balance (if less than $25), or else the greatest of $25 or 1% of the new balance (excluding interest and late fees), plus the interest billed, rounded down to the nearest dollar. Any late fees are then added on to this calculated amount. Moreover, when any interest is due, there is a minimum charge of $1.50.

Question 22.61

31. (Requires a spreadsheet) Suppose that your credit card has an APR of 18% interest rate, corresponding to approximately 1.5% per month. (The actual interest applied is daily interest, at a daily rate of 18%/365; but for simplicity we use a uniform approximate monthly rate. Also, the amount of interest owed depends on exactly when in the month your payment is received.)

Why do we say “approximately” 1.5% per month for an APR of 18%?
How many months will it take to pay off a new balance of $3117.83 by making the minimum payment each month?
How much will you have paid altogether? How much of that is interest?

31.

(a) Months, and billing periods, differ in their numbers of days. Also, the daily interest rate is ; compounded for a 30- day month, the monthly rate is then .

(b) 179 months, or almost 15 years. The first payment is $31 with no interest due, the second payment is $77. Hint: Put the principal in column and the interest due in column . For the interest rounded to the nearest penny, ; for the payment rounded down to the nearest dollar, . Then adjust the last few months’ interest charges by hand to be the minimum $1.50.