Question

A family currently live in an apartment whose monthly rent is $950. They are thinking of buying a house which would cost $220,000. 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 $20,000 and finance the balance through a mortgage at 3.5% 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 2.5% 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 1.

		$42,896
		$44,078
		$42,925
		$43,679

Answer 1

Yearly loan payment is calculated using PMT function in Excel :

rate = 3.5% (annual rate of interest)

nper = 5 (5 year loan with 1 payment each year)

pv = 200000 (loan amount = cost of house - downpayment = $220,000 - $20,000 = $200,000)

PMT is calculated to be $44,296

A7 v х B =PMT(3.5%,5,200000) D E C 7 Т($44,296.27)!

Interest component of 1st year payment = loan amount * annual interest rate

Interest component of 1st year payment = $200,000 * 3.5% = $7,000

After-tax interest cost of 1st year = Interest component of 1st year payment * (1 - tax rate)

After-tax interest cost of 1st year = $7,000 * (1 - 20%) = $5,600

Post tax Mortgage Cost = Yearly loan payment - Interest component of 1st year payment + After-tax interest cost of 1st year

Post tax Mortgage Cost = $44,296 - $7,000 + $5,600

Post tax Mortgage Cost = $42,896