Answer:
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.