BUSINESS, FUR1 2004 VCAA 6 MC

A loan of `$250\ 000` is to be paid back over a period of `20` years at an interest rate of `text(7.4%)` per annum, compounding monthly.
To the nearest dollar, the monthly repayment is closest to

A. $1 963

B. $1 999

C. $2 998

D. $4 343

E. $13 326

Show Answers Only

`B`

Show Worked Solution

`text(Using)\ \ A`	`= PR^n − (Q (R^n − 1))/(R − 1)`
`A`	`= 0`
`P`	`= 250\ 000`
`R`	`= 1 + 7.4/(100 xx 12)`
	`= 1.006167`
`n`	`= 20 xx 12`
	`= 240`

`text(Sub above into equation)`

`0`	`= 250000(1.006167^(240)) − (Q(1.006167^(240) − 1))/(1.006167 − 1)`
`(Q(1.006167^(240) − 1))/0.006167`	`= 250000(1.006167^(240))`
`Q`	`= (250000(1.006167^(240))(0.006167))/(1.006167^(240) − 1)`
	`= $1998.7849…`
	`≈ $1999`

`:.\ text(Monthly repayments are $1999.)`

`=> B`