BUSINESS, FUR1 2003 VCAA 4 MC

Swee borrowed `$150\ 000` at `text(6.2%)` per annum compounding monthly. The repayments are `$1100` per month.
The balance of the loan at the end of five years is closest to

A. $0

B. $84 000

C. $127 000

D. $137 000

E. $148 000

Show Answers Only

`C`

Show Worked Solution

`text(Using)\ \ A = PR^n`

`P = 150\ 000`

`R = 1 + ((6.2/12))/100 = 1.005167`

`n = 5 xx 12 = 60`

`:.\ A`	`= 150\ 000 xx 1.005167^60`
	`= 204\ 354.6788`

`text(Repayments) = (Q(R^n − 1))/(R − 1)`

`text(where)\ Q = 1100`

`:.\ text(Repayments)`	`= (1100(1.005167^60 − 1))/(1.005167 − 1)`
	`= 77\ 143.5993`

`text(Amount owing after 5 years)`

`= A − text(repayments)`

`= 204\ 354.6788 − 77\ 143.5993`

`= $127\ 211.0795`

`=> C`