Question

Joey realizes that he has charged too much on his credit card and has racked up $5,200 in debt. If he can pay $175 each month and the card charges 15 percent APR (compounded monthly), how long will it take him to pay off the debt

Answer 1

it will take approximately 37.38 months to pay off the debt.

Step-by-step explanation:

This can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the debt = $5,200

P = monthly repayment = $175

r = monthly APR = 15% / 12 = 0.15 / 12 = 0.0125

n = number of months required to pay off the debt = ?

Substitute the values into equation (1) and solve for n, we have:

$5,200 = $175 * ((1 - (1 / (1 + 0.0125))^n) / 0.0125)

$5,200 / $175 = (1 - (1 / 1.0125)^n) / 0.0125

29.7142857142857 = (1 - 0.987654320987654^n) / 0.0125

29.7142857142857 * 0.0125 = 1 - 0.987654320987654^n

0.371428571428571 = 1 - 0.987654320987654^n

0.987654320987654^n = 1 - 0.371428571428571

0.987654320987654^n = 0.628571428571429

Loglinearlizing both sides and solving for n, we have:

n log(0.987654320987654) = log(0.628571428571429)

n = log(0.628571428571429) / log(0.987654320987654)

n = -0.201645363528069 / -0.00539503188670629

n = 37.38

Therefore, it will take approximately 37.38 months to pay off the debt.