BUSINESS, FUR1 2005 VCAA 5 MC

An investor borrows `$200\ 000` for five years to buy an apartment.
The interest rate is `text(8.5%)` per annum compounding monthly.
It is an interest only loan, that is, at the end of five years, the investor will still owe `$200\ 000`.
He is required to make monthly repayments.
Correct to the nearest cent, his monthly repayment will be

A. $666.67

B. $1416.67

C. $1757.67

D. $4103.31

E. $6789.95

Show Answers Only

`B`

Show Worked Solution

`text(Using)\ \ A = PR^n − (Q(R^n − 1))/(R − 1) \ \ \ … \ (1)`

`A`	`= 200\ 000`
`P`	`= 200\ 000`
`R`	`= 1 + 8.5/(12 xx 100)`
	`= 1.0070833`
`n`	`= 12 xx 5`
	`= 60`

`text(Sub above values into (1))`

`200\ 000`	`= 200\ 000(1.0070833)^(60) − (Q(1.0070833^(60) − 1))/(1.0070833 − 1)`
`(Q(1.0070833^(60) − 1))/(0.0070833)`	`= 200\ 000(1.0070833)^(60) − 200\ 000`
`(Q(1.0070833^(60) − 1))/(0.0070833)`	`= 200\ 000(1.0070833^60 − 1)`
`Q`	`= 200\ 000 xx 0.0070833`
	`= $1416.66…`
	`≈ $1416.67`

`:.\ text(Monthly payments are $1416.67)`

`=> B`