Question

You just acquired a 30-year mortgage in the amount of $179,500 at 4.75 percent interest, compounded monthly. payments will be equal over the life of the loan with the first payment due one month after the date of the loan. how much of the first payment will be interest?

Answer 1

Given:
Present value, P=179500
interest per period (month), i = 0.0475/12
number of periods (month), n=30*12=360

Interest charged after first month
Interest=P*i
=179500*0.0475/12
=710.52

Monthly payment (just to confirm that A > Interest)
A = Pi(1+i)^n/((1+i)^n-1)
=179500*(0.0475/12)(1+0.0475/12)^360/((1+0.0475/12)^360-1)
= 936.36 (to the nearest cent.
>  710.52   so ok.