Question

Round to the nearest penny.

You owe $2,348.62 on a credit card with an 8.75% APR. You pay $300.00 toward the card at the beginning of the month. What is the difference in interest accrued compared with if you had paid an additional $300.00 more than you had originally intended toward the card?Using the information from Problem 3, how many months will it take you to pay off your debt if you pay $600.00 at the beginning of each month? Include the last month even if the payment is less than $600.00.

Answer 1

Monthly rate = 8.75%/12 = 0.007291666666666667.

1) Difference in interest for the month if you pay $600 instead of $300 at the beginning:
Interest saved = 300 * 0.007291666666666667 = 2.1875 → $2.19 (nearest penny).

2) How many months to pay off if you pay $600 at the beginning of each month:

Start balance: $2,348.62

Month 1
- Pay at beginning: $600.00 → balance = $1,748.62
- Interest (1,748.62 × 0.0072916667) = $12.75
- End balance = $1,761.37

Month 2
- Pay at beginning: $600.00 → balance = $1,161.37
- Interest = $8.47
- End balance = $1,169.84

Month 3
- Pay at beginning: $600.00 → balance = $569.84
- Interest = $4.16
- End balance = $574.00

Month 4
- Pay at beginning: final payoff = $574.00 (less than $600). Loan is paid off; no further interest.

It takes 4 months to pay off the debt.