Question

3.Charles Carr borrowed $3,500 to consolidate his debts. Since Charles had an excellent credit rating, he was able to borrow at a 12% effective annual rate. Charles is required to make monthly payments. Charles will make equal payments for the next 36 months. You are to calculate his monthly payments.

a.What is the corresponding annual percentage rate?

b.Compute his monthly payment.

Answer 1

Answer a.

Effective annual rate = 12.00%

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.12)^(1/12) - 1
Monthly interest rate = 1.0094888 - 1
Monthly interest rate = 0.0094888 or 0.94888%

Annual interest rate = 12 * Monthly interest rate
Annual interest rate = 12 * 0.94888%
Annual interest rate = 11.39%

Answer b.

Amount borrowed = $3,500
Time period = 36 months

Let monthly payment be $x

$3,500 = $x/1.0094888 + $x/1.0094888^2 + … + $x/1.0094888^35 + $x/1.0094888^36
$3,500 = $x * (1 - (1/1.0094888)^36) / 0.0094888
$3,500 = $x * 30.374750
$x = $115.23

Monthly payment = $115.23