Question

You purchased your home 6 years ago. At this time, you took out a mortgage for $200,000, for 30 years, with a fixed rate of 5%. You have made all payments on time but have paid nothing extra on the mortgage. Suppose you sell the house for $210,000 and pay a 6% commission. How much money will you receive (or have to pay) after you pay off your loan?

Solve using a financial calculator.

Answer 1

Assumption: Monthly mortgage payments, which is a customary assumption in case of home loans

Loan amount, PV = - $ 200,000

Time period = nos. of months in 30 years = 12 x 30 = 360

Interest rate = 5% per annum

Rate = interest rate per period = interest rate per month = 5% / 12 =  0.004166667

Calculate monthly payment = PMT (Rate, period, PV) = PMT (i, n, PV) = PMT (0.004166667, 360, - 200000) = $1,073.64

We need to figure out the loan outstanding after six years.

After six year, the loan has 30 - 6 = 24 years to go.

So, the loan outstanding amount should be nothing but present value of all the future monthly payment of $1,073.64 over next 24 years.

Loan outstanding = PV (Rate, period, PMT) = PV (i, n, PMT)

i = 0.004166667 (same as before)

n = number of months in balance 24 years = 12 x 24 = 288

PMT = - $1,073.64

Hence, Loan outstanding = PV (Rate, period, PMT) = PV (i, n, PMT) = PV (0.004166667, 288, -1073.64) = $179,870.62

Sale Value of the house = 210,000

Sale commission = 6% = 6% x 210,000 =  12,600

Money left after you pay off your loan = Sale Value - Sale commission - Loan outstanding

= 210,000 - 12,600 - 179,870.62

= $ 17,529.38