Question

Annuity Payment and EAR

You want to buy a car, and a local bank will lend you $30,000. The loan would be fully amortized over 3 years (36 months), and the nominal interest rate would be 6% with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.
$  

What is the loan's EFF%? Round your answer to two decimal places.
%

Answer 1

Answer a.

Amount borrowed = $30,000
Period = 3 years or 36 months
Annual interest rate = 6%
Monthly interest rate = 0.50%

Let monthly payment be $x

$30,000 = $x/1.005 + $x/1.005^2 + ... + $x/1.005^35 + $x/1.005^36
$30,000 = $x * (1 - (1/1.005)^36) / 0.005
$30,000 = $x * 32.871016
$x = $912.66

Monthly payment = $912.66

Answer b.

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.005)^12 - 1
Effective annual rate = 1.0617 - 1
Effective annual rate = 0.0617 or 6.17%