Question

Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses.


Card A
Card B
Amount
$1,879.58
$861.00
APR
14%
10%
Monthly Payment
$43.73
$18.29

After 5 years, how much will Marcia have saved in interest by consolidating the two balances?
a.
$1,526.40
b.
$2,422.80
c.
$105.00
d.
$227.40

Answer 1

Answer: d. $227.40

Work:
- Card A: total paid = 43.73(60) = 2623.80, interest = 2623.80 − 1879.58 = 744.22
- Card B: total paid = 18.29(60) = 1097.40, interest = 1097.40 − 861.00 = 236.40
- Interest paid if kept separate for 5 years = 744.22 + 236.40 = 980.62

If consolidated at 10% APR for 5 years (n = 60, monthly r = 0.10/12), the required monthly payment is
M = r·PV / [1 − (1 + r)^(−60)] with PV = 2740.58, giving M ≈ $58.23.
- Total paid = 58.23(60) ≈ 3493.80, interest = 3493.80 − 2740.58 = 753.22

Savings in interest = 980.62 − 753.22 = $227.40.