Question

Rachel has developed a plan to start paying off her credit card debt, and has stopped making purchases with her credit card. She has a credit card balance of $1,120.87. Her card has an APR of 14.12%, compounded monthly, and has a minimum monthly payment of 3.15% of the total balance, which is calculated after the monthly interest. Rachel has decided to pay off her debt by making identical monthly payments over a period of two years. If she starts this month, how much greater will her first payment be than the minimum payment required? (Round final answer to the nearest dollar.)
a.
$17
b.
$14
c.
$19
d.
$11

Answer 1

Monthly rate r = 0.1412/12 = 0.0117666667.

Because she starts this month the 24 equal payments form an annuity-due. The payment P satisfies
PV = P * ((1 - (1+r)^-24)/r) * (1+r),
so
P = PV / [((1 - (1+r)^-24)/r) * (1+r)].

Compute:
(1+r)^24 ≈ 1.3246 ⇒ (1+r)^-24 ≈ 0.7547
(1 - (1+r)^-24)/r ≈ 0.2453/0.011766667 ≈ 20.854
Multiply by (1+r): ≈ 20.854 * 1.011766667 ≈ 21.100

Thus P ≈ 1120.87 / 21.100 ≈ $53.13 (first payment).

Minimum payment = 3.15% of balance after one month’s interest = 0.0315 * (1120.87*(1+r))
= 0.0315 * 1134.058 ≈ $35.72.

Difference ≈ 53.13 − 35.72 ≈ $17.41 ≈ $17 (nearest dollar).

Answer: $17 (choice a).