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?

Option A: 10.75% compounded monthly
Option B: 11.50% compounded monthly
Option C: 12.25% compounded monthly
Option D: 13.00% compounded monthly

Answer 1

To determine the greatest interest rate that John can accept and still meet his criteria, we need to calculate the monthly payment for each option and see which one is at or below $150. The greatest interest rate that John can accept is Option A: 10.75% compounded monthly.

Step-by-step explanation:

To determine the greatest interest rate that John can accept and still meet his criteria, we need to calculate the monthly payment for each option and see which one is at or below $150.

Using the compound interest formula, monthly payment = P(r(1+r)^n)/((1+r)^n-1), where P is the principal, r is the monthly interest rate, and n is the number of payments:

Option A: Monthly payment = 4500(0.1075(1+0.1075)^36)/((1+0.1075)^36-1) = $146.81

Option B: Monthly payment = 4500(0.115(1+0.115)^36)/((1+0.115)^36-1) = $150.34

Option C: Monthly payment = 4500(0.1225(1+0.1225)^36)/((1+0.1225)^36-1) = $153.96

Option D: Monthly payment = 4500(0.13(1+0.13)^36)/((1+0.13)^36-1) = $157.78

Therefore, the greatest interest rate that John can accept and still meet his criteria is Option A, with an interest rate of 10.75% compounded monthly.