Question

A family currently live in an apartment whose monthly rent is $1050. They are thinking of buying a house which would cost $250,000. They plan to live in this house for 5 years and sell it at the end of the 5th year. They would put a downpayment of $25,000 and finance the balance through a mortgage at 3% interest rate. The mortgage is to be repaid in 5 annual installments (which include both principal and interest) at the end of each year for the next 5 years The house will have the following additional expenses: annual maintenance: $1500; Property taxes:$5500; Insurance: $1200. Assume they are in tax bracket of 20% and the price of home, rent and expenditure increases by 2% per year. Their opportunity cost or required rate of return is 5% per year. Note that property taxes are tax deductible and there no tax payable on capital gains. Use annual compounding for amortization schedule of mortgage. Calculate the Post tax Mortgage Cost (principal repayment plus after tax interest cost) for year 4.

a. $48,844

b. $44,078

c. $48,296

d. $48,566

Answer 1

  
Cost of house=   250000
down payment =   25000
Loan Amount (P) is = 250000-25000=   225000
interest rate =   3.00%
  
Number of years of Repayment (n)=   5
Equal payment formula = P*i/(1-((1+i)^-n))  
225000*3%/(1-((1+3%)^-5))  
$49,129.78

Number of Payment left after 3 years (n)=   2
Unpaid balance at time (n) formula = Equal payment *(1-((1+i)^-n))/i  
49129.78*(1-((1+3%)^-2))/3%  
  
94008.34518  
  
Interest for period 4 = Balance at year 3*interest rate  
94008.3451786219*3%  
2820.250355  
Tax benefit of interest @20% (ordinary tax rate)= 2820.250355*20%=   564.0500711
After-tax mortgage cost = Mortgage equal payment - Tax benefits of interest cost  
49129.78-564.05  
$48,565.73  
  

So Answer is d, $48566