Question

A couple took out a 30-year mortgage 10 years ago. At that time, the mortgage was $306,800.00, with 7.44% APR and monthly compounding of interest. Today, the couple has been offered $327,700.00 for their house. If the couple accepts the offer, how much cash will they take from the deal? The cash will be the difference between the sell price and what is owed on the loan.

Answer 1

Step 1
First calculate the monthly loan payment on mortgage of $306800 using present value of annuity formula
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = 306800
P = monthly loan payment = ?
r = rate of interest per month = 7.44%/12 = 0.0062
n = no.of months repayment = 30 years * 12 = 360
306800 = P * {[1 - (1+0.0062)^-360]/0.0062}
306800 = P * 143.862
P = 2132.60
Monthly Loan payment = $2132.60
Step 2
Second step is to find out the outstanding loan balance at the end of 10th year using present value of annuity formula
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = ?
P = monthly loan payment = 2132.60
r = rate of interest per month = 7.44%/12 = 0.0062
n = no.of months repayment remaining = 20 years * 12 = 240
Present value of annuity = 2132.60 * {[1 - (1+0.0062)^-240]/0.0062}
Present value of annuity = 2132.60 * 124.70
Present value of annuity = 265933.89
Loan amount owed after 10 years = $2,65,933.89
Step 3
Answer
Amount of cash couple will take from the deal = Sell price - Amount owed on loan
Amount of cash couple will take from the deal = $327700 - $265933.89 = $61,766.11