Question

John is planning to take out a personal loan for $4,500 to buy a car. He would like to keep his monthly payments at or below $150.00 and pay the loan off in three years. Which of the following is the greatest interest rate John can accept and still meet his criteria?
a. 10.75% compounded monthly
b. 11.50% compounded monthly
c. 12.25% compounded monthly
d. 13.00% compounded monthly

Answer 1

. 12.25% compounded monthly

Answer 2

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.