Question

Listed below are the balances and annual percentage rates for Jimmy's credit cards. If Jimmy makes the same payment each month to pay off his entire credit card debt in the next 12 months, how much will he have paid in interest in the 12 month period?(Hint, find out how much interest Jimmy pays to each card over the 12 months seperately, and then add them together.)
Credit Card
Current Balance
APR
A
$563.00
16%
B
$2,525.00
21%
C
$972.00
19%


a.
$321.83
b.
$370.75
c.
$449.24
d.
$730.80

Answer 1

Compute each card's monthly payment that amortizes its balance in 12 months, then interest for that card = (12 × monthly payment) − starting balance. Sum the three interests.

Monthly rate = APR/12.
- A: r = 0.16/12 = 0.0133333. Monthly payment = P·r / (1 − (1+r)^−12) = 563·0.0133333/(1−(1.0133333)^−12) ≈ $51.02. Interest = 12·51.02 − 563 ≈ $49.24.
- B: r = 0.21/12 = 0.0175. Monthly payment ≈ 2525·0.0175/(1−(1.0175)^−12) ≈ $234.74. Interest = 12·234.74 − 2525 ≈ $291.96.
- C: r = 0.19/12 = 0.0158333. Monthly payment ≈ 972·0.0158333/(1−(1.0158333)^−12) ≈ $89.51. Interest = 12·89.51 − 972 ≈ $108.04.

Total interest ≈ 49.24 + 291.96 + 108.04 = $449.24.

Answer: c. $449.24