Question

You are deciding between two car loans. Both loans would allow you to borrow $25,000 for six years. Loan A charges 3.5% APR compounded monthly. Loan B charges 3% APR compounded continuously. Which loan requires the lowest monthly payment?

Answer 1

(A/P, i%,n) = i((1 + i)^n)/((1 + i)^n-1)

t = 6 * 12 = 72 months

interest per month on first loan = 3.5%/12 = 0.2916667%

interest per month on second loan = 3% / 12 = 0.25% per months compounded continously

Effective interest rate on second loan per month = e^0.0025 - 1 = 0.002503128 = 0.2503128 %

monthly loan payment in first case = 25000 * (A/P, 0.2916667%,72)

= 25000 * 0.015418

= 385.46

monthly loan payment in second case = 25000 * (A/P, 0.2503128 %,72)

= 25000 * 0.015195

= 379.88

As monthly loan is less in second case, it should be selected