An investor buys a property for $640,000 with a 25-year mortgage and monthly payments at a quoted APR of 8%.After 18 months the investor resells the property for $712,000.How much cash will the investor have made from the sale,once the mortgage is paid off?

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly mortgage payment:
P = (PV * r)/(1 - (1+r)^(-n))
Where:
PV = Present value of the loan (640,000)
r = monthly interest rate (8% divided by 12 months)
n = total number of payments (25 years * 12 months per year)

r = 0.08/12 = 0.006666667
n = 25*12 = 300

P = (640000 * 0.006666667)/(1 - (1+0.006666667)^(-300)) = $4,723.29 per month

After 18 months, the investor has paid:
18 * $4,723.29 = $85,019.22

The remaining balance on the mortgage after 18 months is:
PV = (PMT/(r))(1-(1+r)^(-n)) (the formula to calculate the present value of an annuity)
Where:
PMT = monthly payment ($4,723.29)
r = monthly interest rate (0.006666667)
n = total number of payments (25 years * 12 months per year - 18 months already paid)

n = 282

So, PV = (4723.29/0.00666667)(1-(1+0.00666667)^(-282)) = $576,056.51

The investor will receive from the sale:
Sale price - remaining mortgage balance = $712,000 - $576,056.51 = $135,943.49

However, the investor also needs to pay off the mortgage and has already paid $85,019.22. So, the total cash made from the sale is:
$135,943.49 - $85,019.22 = $50,924.27

But the question is asking for the cash made from the sale once the mortgage is paid off, so we need to subtract the remaining balance on the mortgage that will be paid off from the sale price:
$50,924.27 - $576,056.51 = $85,082.24

Therefore, the correct answer is C, $85,082.

An Investor Buys a Property for $640,000 with a 25-Year