Question

Part A
You owe $1,842.66 on a credit card at a 14.5% APR. You pay $250.00 at the beginning of the month and put another $250.00 in a savings account at a 4.0% APR. What is the difference in the amount of interest accrued between the credit card and savings account by the end of one month?
Part B
Using the difference in interest between the credit card and savings account from Part A, how much total interest could you save by putting all $500.00 instead of just $250.00 toward the credit card at the beginning of the month?

Answer 1

Part A

Credit-card monthly rate = 0.145/12 = 0.0120833333.
Savings monthly rate = 0.04/12 = 0.0033333333.

After paying $250 at the start of the month, card balance = 1,842.66 − 250 = 1,592.66.
Interest charged on the card for the month = 1,592.66 × 0.145/12 = $19.24 (≈ $19.2446).

$250 put into savings at the start of the month earns = 250 × 0.04/12 = $0.83 (≈ $0.8333).

Difference (interest charged − interest earned) = 19.2446 − 0.8333 ≈ $18.41.

Part B

If you instead put the full $500 on the card at the start, balance = 1,842.66 − 500 = 1,342.66.
Interest on the card then = 1,342.66 × 0.145/12 ≈ $16.22.

Net interest saved by putting the extra $250 on the card this month = $18.41 − $16.22 ≈ $2.19.

(You can also get this directly: monthly rate difference = (0.145−0.04)/12 = 0.00875; savings = 250 × 0.00875 = $2.1875 ≈ $2.19.)