444,772 views
19 votes
19 votes
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

User Yogesh Lakhotia
by
2.8k points

1 Answer

21 votes
21 votes

Answer:

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

Step-by-step 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.

User Inkooboo
by
3.1k points