Question

Another family has been paying down their home for 25 years with 5 more years left on the mortgage. Their monthly payment is $861 and the interest rate is 8.01% compounded monthly. They want to pay off the home. Find the payoff amount with 5 years left on the mortgage.

Answer 1

Step 1: Find the loan amount:

We can use the present value of the annuity formula to find the loan amount.

Where,
PVA = Present value of the annuity
A = Montly payment
i = Interest rate in decimal form (i.e 8.01% = 0.0801)
n = Number of years
a = Number of payments in a year

Step 2: Find the balance of the loan after 20 years i.e 240th payment.

Balance of loan formula:

Where,
PV = Present value / original balance
A =Monthly payment
i = rate of interest
a = Number of payments in a year
n = number of years
na = total number of payments

Therefore, the payoff amount with 5 years left on the mortgage is $42,453.15.