Question

A $92,000 mortgage has an interest rate of 9% compounded semi-annually for a 5 year term. The mortgage is amortized over 20 years. What is the monthly payment?

Answer 1

Mortgage amount = 92000

Effective rate of interest = (1+r/2)^2-1

= (1+ 0.09/2)^2-1

= 0.0920 = 9.2%

Effective monthly interest rate = 0.092/12= 0.007668

monthly payment for 20 yrs, n = 12*20= 240 months

monthly payment= present value * {i*(1+i)^n/((1+i)^n-1)}

=92000*{0.007668*1.007668^240/(1.007668^240-1)}

= 92000* {0.007668*6.25449/(6.25449-1)}

= 92000*0.047959/5.25449

= 839.713

You can also use PMT(0.7668%,240,92000) in excel. Its a formula for getting monthly payment of a loan.