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.

ans.

heterothermic organisms include those organisms that can switch between homeothermic (having body temperature higher than environment) and poikilothermic (having variation in internal body temperature) strategies.

some migratory birds show heterothermy as they decrease their metabolic rate during cold nights to keep their body temperature low. drop in metabolic rate allows increase in production efficiency of birds that reduces the internal body temperature to make it equal to external cold temperature during cold nights.

thus, the correct answer is 'birds allow their temperature drop in order to increase their production efficiency.'