Question

We are considering investing in a house that will cost $460,000 and generate weekly rental income of $440.

Calculate the value of our investment ftve years from today, assuming that we fund our investment using a $150,000 cash down payment and a five-year interest-only loan for the balance. This loan incurs interest of 6.1% per annum. We deposit all excess cash in a bank account that earns interest of 2.4% per annum compounded monthly.

Make the following additional assumptions, which are the same ones made in class:

• There are no taxes.

• The house price is constant over the five years of our investment.

• All rent and interest payments and receipts occur in a lump sum at the end of each year.

• There are 52 weeks in a year.

Answer 1

Effective Interest rate on the bank deposit(EAR) = (1+ annual rate/n)ⁿ - 1 {where n = number of compounding periods}

EAR = (1 + 0.024/12)¹² - 1 = (1 + 0.002)¹² - 1 = 2.43% or 2.4%(for easy calculations as there is not much difference)

Year	Annual Rental Income (440*52)	Pricipal Repayment	Interest payment(6.1-2.4=3.7%)	Total
0		(150000) (Down payment)		(150000)
1	22880	(62000)	(11470)	(50590)
2	22880	(62000)	(9176)	(48296)
3	22880	(62000)	(6882)	(46002)
4	22880	(62000)	(4588)	(43708)
5	22880	(62000)	(2294)	(41414)
				(380010)

Interest is received and paid in the end of the year at the same amount. Therefore, the difference between the rates is taken.

The annual principal repayment = (460000-150000)/5 = 62000

Interest Schedule

Year	Amount at which interest is paid	Interest (6.1-2.4=3.7%)
1	310000	(11470)
2	310000-62000=248000	(9176)
3	248000-62000=186000	(6882)
4	186000-62000=124000	(4588)
5	124000-62000=62000	(2294)

The price of house after 5 years = $460000

The total payments including principal repayments and rental income = $380010

Therefore, the value of our investment after 5 years = 460000-380010 = $79990