You have just borrowed $20,000 to buy a new car.The loan agreement calls for 60 monthly payments of $444.89 each to begin one month from today.If the interest is compounded monthly,then what is the effective annual rate on this loan?

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) can be calculated using the formula for the EAR from a monthly compounded interest rate. Given the monthly payment and the loan amount, we can first find the monthly interest rate and then convert it to an EAR. The monthly rate that turns $20,000 into 60 payments of $444.89 is approximately 1% (this can be found using the formula for the present value of an annuity). The EAR is calculated as (1 + monthly rate)^12 - 1. Plugging in 0.01 for the monthly rate gives an EAR of approximately 12.68%.

You Have Just Borrowed $20,000 to Buy a New Car