An investor buys a property for $ 603 comma 000 with a 25-year mortgage and monthly payments at 7.9 % APR. After 18 months the investor resells the property for $ 661 comma 615. How much cash will the investor have made from the sale, once the mortgage is paid off?

The investor have made $70,888 from the sale of property.

Explanation:

The information provided is as follows:

25 year mortgage value = $603,000

Annual percentage rate (APR) = 7.9%

Annual percentage rate (APR) (in months) = (7.9%:12) = 0.6583%

Resale value after 18 months = $661,615

Mortgage tenure in months = 25 years * 12 = 300 months

Remaining period of mortgage at the date of resale = (300 months - 18 months) = 282 months

Step 1:

Calculate the present value annuity factor (PVAF) at 0.6583% for 300 months:

PVAF (₀.₀₀₆₅₈₃,₃₀₀) = [1 - (1 / (1+interest rate) ³⁰⁰] : Interest rate

PVAF (₀.₀₀₆₅₈₃,₃₀₀) = [1 - (1 / (1+0.006583)) ³⁰⁰] : 0.006583

PVAF (₀.₀₀₆₅₈₃,₃₀₀) = 130.6887

Therefore, the PVAF (₀.₀₀₆₅₈₃,₃₀₀) is 130.6887.

Step 2:

Calculate the equated monthly installment (EMI) as follows:

EMI = Mortgage value : PVAF (₀.₀₀₆₅₈₃,₃₀₀)

EMI = 603,000 : 130.6887

EMI = 4614.018

Step 3:

Calculate the present value annuity factor (PVAF) at 0.6583% for 282 periods:

PVAF (₀.₀₀₆₅₈₃,₂₈₂) = [1 - (1 / (1+interest rate) ²⁸²] : Interest rate

PVAF (₀.₀₀₆₅₈₃,₂₈₂) = [1 - (1 / (1+0.006583)) ²⁸²] : 0.006583

PVAF (₀.₀₀₆₅₈₃,₃₀₀) = 128.0288

Therefore, the PVAF (₀.₀₀₆₅₈₃,₃₀₀) is 128.0288.

Step 4:

Calculate the present value of the mortgage on the date of resale of property:

PV of mortgage at date of resale = EMI * PVAF (₀.₀₀₆₅₈₃,₂₈₂)

PV of mortgage at date of resale = 4614.018 * 128.0288

PV of mortgage at date of resale = $590,727.1

Step 5:

Calculate the profit from the resale of the property:

Profit on resale = Resale value - Present value of mortgage

Profit on resale = $661,615 - $590,727.1

Profit on resale = $70,887.87

Profit on resale = $70,888 (rounded off value)

Therefore, the investor has made $70,888 from the sale of property.