Question

You want to buy a car, and a local bank will lend you $35,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 10% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

Answer 1

Amount borrowed = $35,000
Annual interest rate = 10%
Monthly interest rate = 0.8333%
Period = 60 months

Let monthly payment be $x

$35,000 = $x/1.008333 + $x/1.008333^2 + ... + $x/1.008333^59 + $x/1.008333^60
$35,000 = $x * (1 - (1/1.008333)^60) / 0.008333
$35,000 = $x * 47.065805
$x = $743.64

Monthly payment = $743.64

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.008333)^12 - 1
Effective annual rate = 1.1047 - 1
Effective annual rate = 0.1047 or 10.47%