Answer:
The investor have made $70,888 from the sale of property.
Step-by-step 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.