Answer:
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.
