credit card APR

Question

You have a balance of $2100 on your Visa credit card. Assume that you make no more charges on the card and that the card charges 9.6% APR and requires a minimum payment of 3% of the balance. Assume also that you make only the minimum payments.

Find a formula for the balance B after t monthly payments

Answer 1

let's assume that we have equal number of days per month.

So, monthly interest = 9.6% / 12 = 0.8%

Your balance will be increased by 1+0.008=1.008 per month.

Hence after t month your balance increased by: 1.008^t

You make a minimum payment of 3% so at the end of each month your balance will be decreased by factor of 1-0.03 = 0.97.

Hence, after t month your balance decreased by: 0.97^t

your balance after t month:

B = 2100 * 1.008^t * 0.97^t

B = 2100 * (1.008 * 0.97)^t

B = 2100 * 0.97776^t

Hope this helps you.