The annual interest rate on a credit card is 13.99%. If a payment of $400.00 is made each month, how many months will it take to pay off an unpaid balance of $2 comma 455.44? Assume that no new purchases are made with the credit card.

There will be 7 months of repayment for fully paying-off the outstanding amount.

Explanation:

We apply the present value formula to calculate the number of month it takes to paid off the outstanding amount.

We have:

Monthly payment = $400; Discounting period = number of months needs to paid off the amount; Discount rate = 13.99%/12

So, we have: 2,455.44 = [400/(13.99%/12)] x [1 - (1+13.99%/12)^(-n)] <=> [1 - (1+13.99%/12)^(-n)] = 0.071566 <=> (1+13.99%/12)^(-n) = 0.928434 =  <=> n = 6.4

=> There will be 7 months of repayment for fully paying-off the outstanding amount.

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