smc-605-30-Stamp duty

Tania purchased a house for $300 000.

She will have to pay stamp duty based on this purchase price.

Stamp duty rates are listed in the table below.

Calculate the amount of stamp duty that Tania will have to pay. (1 mark)
Assuming that her house will increase in value at a rate of 3.17% per annum, what will the value of Tania's house be after 5 years?

Write your answer to the nearest thousand dollars. (1 mark)

Tania bought her house at the start of 2011.

If the rate of increase in value remains at 3.17% per annum, at the start of which year will the value of Tania's house first exceed $450 000? (2 marks)

Show Answers Only

`$13\ 070`
`$351\ 000`
`2024`

Show Worked Solution

a.	`text(Stamp duty)`	`= 2870 + 6text(%) xx (300\ 000 – 130\ 000)`
		`= $13\ 070`

♦♦ Part (a) was “poorly answered” although exact data is unavailable.
MARKER’S COMMENT: A majority of students did not understand how to use the table.

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

`text(Value)`	`= 300\ 000(1.0317)^5`
	`= 350\ 661.7…`
	`= $351\ 000\ \ text{(nearest $1000)}`

c. `text(Find)\ n\ text(when)\ \ \ A > $450\ 000`

`300\ 000 xx 1.0317^n`	`= 450\ 000`
`n`	`~~12.99…`

MARKER’S COMMENT: Many students who correctly found `n` lost a mark by failing to identify the exact year.

`:.\ text(After 13 years, in 2024, the house value)`

`text(will be over)\ $450\ 000.`

`text(6% of 85 000)`	`= 0.06 xx 85\ 000`
	`= 5100`
`:.\ text(Stamp duty)`	`= 2560 + 5100`
	`= $7660`

CORE*, FUR2 2011 VCAA 3

CORE*, FUR1 2007 VCAA 4 MC