BUSINESS, FUR1 2003 VCAA 9 MC

Peter borrows `$80\ 000` for `10` years at `text(5.6%)` per annum, compounding monthly, with monthly repayments of `$555`.
Which one of the following statements is true?

A. The loan will be fully paid out in ten years.

B. At the end of five years, the balance of the loan will be `$40\ 000`.

C. The amount of interest paid each month during the loan increases.

D. Weekly repayments of `$132` compounding weekly would reduce the period of the loan.

E. If one extra payment of `$2000` is to be made, it would be better to make it at the end of year eight than at the end of year two.

Show Answers Only

`D`

Show Worked Solution

`text(Consider)\ A`

`text($ paid after 10 years)`

`= 555 xx 12 xx 10`

`= $66\ 600`

`text{(less than loan of $80 000)}`

`:.\ text(False, eliminate)\ A`

`text(Consider)\ B`

`text(Total repaid after 5 years)`

`= $66\ 600 -: 2\ \ text{(from}\ A\ text{above)}`

`= $33\ 300`

`text(Principle owing)`

`= (80\ 000 − 33\ 300) + text(interest on loan)`

`= $46\ 700 + text(interest on loan)`

`:.\ text(False, eliminate)\ B`

`text(Consider)\ C`

`text(Monthly repayments are higher than)`

`text(monthly interest, so balance owed)`

`text(decreases monthly.)`

`text(Hence, monthly interest decreases.)`

`:.\ text(False, eliminate)\ C`

`text(Consider)\ D`

`text(Weekly payment of $132 is the same)`

`text(as monthly payments of $572, and there)`

`text(there is also extra benefit of compounding)`

`text(weekly to reduce the period of the loan.)`

`:.\ text(True)`

`text(Similarly)\ E\ text(can be eliminated)`

`=> D`