Joey realizes that he has charged too much on his credit card and has racked up $5,100 in debt. If he can pay $125 each month and the card charges 18 percent APR (compounded monthly), how long will it take him to pay off the debt

It will take Joey 63.59 months to pay off the debt.

Explanation:

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

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

Where;

PV = Present value or debt amount = $5,100

P = Monthly payment = $125

r = annual percentage rate (APR) / 12 = 18% / 12 = 0.18 / 12 = 0.015

n = number of months it will take Joey to pay off the debt = ?

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

5100 = 125 * ((1 - (1 / (1 + 0.015))^n) / 0.015)

5100 / 125 = (1 - (1 / 1.015)^n) / 0.015

40.80 * 0.015 = 1 - 0.985221674876847^n

0.985221674876847^n = 1 - 0.612

0.985221674876847^n = 0.388

loglinearize both sides, we have:

nlog0.985221674876847 = log0.388

n = log0.388 / log0.985221674876847

n = -0.411168274405793 / -0.00646604224923186

n = 63.59

Therefore, it will take Joey 63.59 months to pay off the debt.

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