Question

Suppose a $75,500 mortgage is to be amortized at 6.5% interest. Find the total amount of interest that would be paid for a 40 year term. What is the amount of interest for a 40 year mortgage?

Answer 1

Use the formula of the present value of annuity ordinary to find the monthly payment of the loan
The formula is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 75500
PMT monthly payment?
R interest rate 0.065
K compounded monthly 12
N time 40 years
So we need to solve for pmt
PMT=Pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=75,500÷((1−(1+0.065÷12)^(
−12×40))÷(0.065÷12))
=442.02 (this is the monthly payment)

Now find the amount of interest
Total interest=total paid-present value

Present value=75500
Total paid
442.02×12months×40years
=212,169.6

Total interest=212,169.6−75,500
=136,669.6

The answer is 136,669.6