Question

Raul Peters expects to need $50 000 as a deposit on a house in the suburb of Bayswater in 6-years time, and he can invest today in an account paying 7.25% p.a. He has just seen a cheaper house in the suburb of Riverview which will require an amount of $40 000 as a deposit on a house in 5-years time, and the owner of this cheaper house has offered him to invest any savings from today in an account paying 9% p.a., compounded monthly.

Required:

Given that he wants to fund a house purchase with an initial investment that will grow to the amount of the deposit at the required time, approximately how much lower would Raul Peters initial investment be for the house in Riverview rather than in Bayswater?

Answer 1

House in Suburb of Bayswater:

FV = Deposit Required = $50,000

r = interest rate = 7.25%

n = 6 years

Initial Investment required = FV / (1+r)^n

= $50,000 / (1+7.25%)^6

= $50,000 / 1.52189189843

= $32853.8446466

= $32,853.84

House in Suburb of Riverview:

FV = Deposit Required = $40,000

r = interest rate = 9%

n = 5 years

Initial Investment required = FV / (1+r)^n

= $40,000 / (1+9%)^5

= $40,000 / 1.5386239549

= $25,997.2554519

= $25,997.26

Difference in Initital Investment = Initial investment of house in suburb of Basewater - Initial investment of house in suburb of Riverview

= $32,853.84 - $25,997.26

= $6,856.58

Therefore, initital investment would be lower by $6,856.58 for house in Riverview than house in Basewater