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

First find how much interest she now pays over 5 years.

Total monthly payment now = 43.73 + 18.29 = 62.02.
Total paid in 5 years = 62.02 × 60 = 3,721.20.
Total principal = 1,879.58 + 861.00 = 2,740.58.
Interest now = 3,721.20 − 2,740.58 = 980.62.

If she consolidates at 10% APR, the monthly rate is r = 0.10/12.
The monthly payment to amortize $2,740.58 in 60 months is
PMT = P · r / (1 − (1 + r)^(−60)) ≈ $58.23.

Total paid in 5 years after consolidation ≈ 58.23 × 60 = 3,493.80.
Interest after consolidation ≈ 3,493.80 − 2,740.58 = 753.22.

Interest saved = 980.62 − 753.22 = 227.40.

Answer: d. $227.40.