BUSINESS, FUR1 2002 VCAA 4 MC

Rho takes a `20`-year loan of `$172\ 000` at `text(6%)` per annum, compounding monthly and with monthly repayments.
To fully repay the loan in `20` years, the amount he must repay each month is

A. $716.67

B. $1216.54

C. $1232.26

D. $9058.63

E. $10 320.00

Show Answers Only

`C`

Show Worked Solution

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

`P`	`= 172\ 000`
`R`	`= 1 + 6/(12 xx 100)`
	`= 1.005`
`n`	`= 20 xx 12`
	`= 240`

` text(After 20 years,)\ A = 0`

`:.\ text{Sub above into (1)}`

`0 =`	`(172\ 000)(1.005)^240 − (Q(1.005^240− 1))/(1.005 − 1)`
`(Q(1.005^240− 1))/0.005 =`	`(172\ 000)(1.005)^240`
`Q =`	`((172\ 000)(1.005^240)(0.005))/(1.005^240 − 1)`
`=`	`$1232.261…`

`:.\ text(Monthly repayments are $1232.26)`

`=> C`