Question

You have just arranged for a $200,000 mortgage to finance the purchase of a house. The mortgage has an 8 percent quoted rate, interest is compounded semi-annually and it calls for monthly payments for the next 20 years. What is the monthly payment?Please provide step-by-step instructions for solving the problem

Answer 1

Annual interest rate = 8.00%
Semiannual interest rate = 4.00%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.04)^2 - 1
Effective annual rate = 1.0816 - 1
Effective annual rate = 0.0816 or 8.16%

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.0816)^(1/12) - 1
Monthly interest rate = 1.006558 - 1
Monthly interest rate = 0.006558 or 0.6558%

Amount borrowed = $200,000
Time period = 20 years or 240 months

Let monthly payment be $x

$200,000 = $x/1.006558 + $x/1.006558^2 + … + $x/1.006558^239 + $x/1.006558^240
$200,000 = $x * (1 - (1/1.006558)^240) / 0.006558
$200,000 = $x * 120.722960
$x = $1,656.69

Monthly payment = $1,656.69