Isaac realizes that he charged too much on his credit card and has racked up $7,000 in debt. If he can pay $275 each month and the card charges 17.55% APR (compounded monthly), how long will it take him to pay off the credit card? How much interest expense will Isaac pay during this time?

Question

Quizplus · Accepted Answer

To find out how long it will take Isaac to pay off his credit card, we can use the formula for the present value of an annuity:

PV = R[(1 - (1 + r)^-n)/r]

where:
PV = present value (in this case, $7,000)
R = monthly payment ($275)
r = monthly interest rate (APR divided by 12, so 17.55%/12 = 0.014625)
n = number of months

Plug in the values and solve for n:

$7,000 = $275[(1 - (1 + 0.014625)^-n)/0.014625]
25.45454545 = (1 - (1 + 0.014625)^-n)/0.014625
0.365463421875 = (1 + 0.014625)^-n
n = log(0.365463421875)/log(1.014625)
n ≈ 32.07

So it will take Isaac about 32.07 months to pay off his credit card.

To find out how much interest expense Isaac will pay during this time, we can subtract the original balance from the total amount paid:

Total paid = $275 x 32.07 = $8,819.25
Interest expense = $8,819.25 - $7,000 = $1,819.25

Therefore, the best choice is B, which matches the correct number of months and interest expense.

Isaac Realizes That He Charged Too Much on His Credit