Answer: C. 12.25% compounded monthly
Step-by-step explanation:
Since, the monthly payment formula for a loan is,
\(P = \frac{(PV)r}{1-(1+r)^{-n}}\)
Where PV is the principal value of the loan,
r is the rate per month,
n is the number of months,
Here, PV = $ 4,500, n = 36,
Let r be the annual rate of interest,
P ≤ 150
⇒ \(\frac{(4500)\frac{r}{12}}{1-(1+\frac{r}{12})^{-36}}\leq 150\)
⇒ \(375 r \leq 150-150(1+\frac{r}{12})^{-36}\)
⇒ \(r\leq 0.1225\)
Thus, the greatest annual interest rate = 0.1225 = 12.25 %
⇒ Option C is correct.
