Question

June has a credit card balance of $4,350 that comes with a 19% APR. She would like to have the balance paid off in the next 8 months, but she is having trouble making the monthly payments required to do so. In order to lower her monthly payments, she decides to sell her porcelain doll collection for $2,000 to apply directly to her credit card balance. June still wants to pay off the balance in 8 months. By applying the doll money, how much has June lowered her minimum monthly payment?
a.
$145.62
b.
$268.14
c.
$315.06
d.
$583.20

Answer 1

Monthly rate = 0.19/12 = 0.0158333. The monthly payment to amortize a balance P in n = 8 months is
payment = P * [i(1+i)^n]/[(1+i)^n − 1].

Compute the annuity factor for i = 0.0158333 and n = 8: ≈ 0.134083.

So payment before selling dolls = 4350(0.134083) ≈ $583.27.
Payment after applying $2000 (balance = 2350) = 2350(0.134083) ≈ $315.13.

Reduction = 583.27 − 315.13 ≈ $268.14.

Answer: b. $268.14.