Question

Assume that you have a balance of $5000 on your Visa credit card and that you make no more charges. If your APR is 22% and each month you make only the minimum payment of 3% of your balance, then find a formula for the balance after t monthly payments.

A) 5000(0.952217)t

B) 5000(1.011117)t

C) 5000(0.987783)t

D) 5000(1.048883)t

Can someone explain to me how to solve this please

Answer 1

C) 5000(0.987783)^t

Explanation:

The monthly interest rate is the APR divided by 12, so is 22%/12 ≈ 0.018333.

Each month, the previous balance (B) has interest charges added to it, so the new balance is ...

balance with interest charges = B + (22%)/12×B = 1.018333×B

The minimum payment is 3% of this amount, so the new balance for the next month is ...

balance after payment = (1.018333B)(1 - 0.03) = 0.987783B

Since the balance is multiplied by 0.987783 each month, after t payments, the balance starting with 5000 will be ...

5000×0.987783^t . . . . . . . . . matches choice C