What is the balance on the card after eight years

Question

You have a credit card with an APR of 36%. The card requires a minimum monthly payment of 5% of the balance. You have a balance of $7000. You stop charging and make only the minimum monthly payment. What is the balance on the card after eight years? (Round your answer to the nearest cent.)

Answer 1

The APR is 36% so the monthly interest is %3.

A minimum payment of 5% is required every month.

The monthly change in balance is the payment minus the interest = 5% - 3% - 2%.

Each month the balance decreases by 2%: balance for month + 1 = balance for month x 0.98

Months = 12 x 8 = 96.

Balance after 8 years = $7000 x (0.98) ^ 96 = $7000 x 0.14378 = $1006.47 to the nearest penny.