Question

An $600,000 Mortgage is amortized by monthly payments over 25 years. The interest rate charged is 4% compounded semi-annually.

1.What is the size of the monthly payment to the nearest dollars?

2.How much interest paid in the first payment?

3.What is the outstanding balance after the first payment?

Answer 1

PV =$600000=present value

n =25*12=300=number of deposits

i = interest rate of compounding period=(1+r/m)^m/12-1 r=rate provided

m=frequeancy of compounding

= (1+0.04/2)^2/12-1

i =0.00330589

R=Regular deposit/Monthly Payement= PV*i/[1-(1+i)^-300]

(600000*0.00330589)/[1-(1+0.00330589)^-300]

=$3156.12

1.The monthly payment will be $3156.12

The percentage of interest on total amount payable is

(946836-600000)/946836*100=36.63%

Interest paid in the first payment is=$3156.12*36.63%=$1156.09

Balance after first payment is=$946836-3156.12=$943679.88