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

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

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.

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