smc-817-10-Compounded Value of $1 Table

v1 Financial Maths, STD2 F4 2013 HSC 26e

Lucas invests $5000.

Interest is compounded half-yearly at a rate of 3% per half-year.

Use the table to calculate the value of his investment at the end of 4 years. (2 marks)

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`$6335`

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♦ Mean mark 44%
COMMENT: Structure your answer: 1-Find the interest rate per compounding period (same in this case). 2-Find the number of compounding periods..

`r =\ text(3% per half-year)`

`n = 8 \ \ \ \ text{(8 half-years in 4 years)}`

`⇒ \text{Table Factor} = 1.267`

`text(Investment)`	`= 5000 × 1.267`
	`= $6335`

`:.\ \text{After 4 years, investment value is } $6335`

v1 Financial Maths, STD2 F4 2018 HSC 19 MC

The table shows the compounded values of $1 at different interest rates over different periods.

Ben hopes to have $18 000 in 2 years to travel. He opens an account today which pays interest of 4% p.a., compounded quarterly.

Using the table, which expression calculates the minimum single sum that Ben needs to invest today to ensure he reaches his savings goal?

18 000 × 1.0816
18 000 ÷ 1.0816
18 000 × 1.0829
18 000 ÷ 1.0829

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`text(D)`

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`text(4% annual)`

`= (4%)/4 = 1% per quarter`

`2 \ text(years) = 8 \ text(periods)`

`\text(From the table: at 8 periods and 1%, compounded value) = 1.0829`.

`:.\ text(Minimum sum) = 18\ 000 ÷ 1.0829`

`=>\ text(D)`

v1 Financial Maths, STD2 F4 2016 HSC 8 MC

The table shows the future value of an investment of $1000, compounding yearly, at varying interest rates for different periods of time.

Based on the information provided, what is the future value of an investment of $3500 over 5 years at 2% pa?

$1554.80
$2835.72
$3864.28
$4312.36

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`=> C`

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`text(Table factor) = 1104.08`

`:. FV`	`= 3.5 xx 1104.08`
	`= $3864.28`

`=> C`

Financial Maths, STD2 F4 2018 HSC 19 MC

The table shows the compounded values of $1 at different interest rates over different periods.

Amy hopes to have $21 000 in 2 years to buy a car. She opens an account today which pays interest of 4% pa, compounded quarterly.

Using the table, which expression calculates the minimum single sum that Amy needs to invest today to ensure she reaches her savings goal?

21 000 × 1.0816
21 000 ÷ 1.0816
21 000 × 1.0829
21 000 ÷ 1.0829

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`text(D)`

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`text(4% annual)`

♦♦ Mean mark 33%.

`=> (4%)/4 = 1text(% compounded quarterly)`

`=> n = 8`

`=>\ text(Factor) = 1.0829`

`:.\ text(Minimum sum) = 21\ 000 ÷ 1.0829`

`=>\ text(D)`

Financial Maths, STD2 F4 2016 HSC 8 MC

The table shows the future value of an investment of $1000, compounding yearly, at varying interest rates for different periods of time.

Based on the information provided, what is the future value of an investment of $2500 over 3 years at 4% pa?

$1124.86
$2812.15
$3624.86
$5312.15

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`=> B`

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`text(Table factor) = 1124.86`

`:. FV`	`= 2.5 xx 1124.86`
	`= $2812.15`

`=> B`

Financial Maths, STD2 F4 2011 HSC 23c

An amount of $5000 is invested at 10% per annum, compounded six-monthly.

Use the table to find the value of this investment at the end of three years. (2 marks)

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`$6700`

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♦♦ Mean mark 28%
MARKER’S COMMENT: Remember that the number of periods is the number of “compounding periods” and when asked to use the table, use the table!

`text(Interest rate)= text(10% pa)= text(5% per 6 months)`

`text(Period)= 6\ \ \ \ text{(6 x 6 months in 3 years)}`

`=> text(Table value)=1.340`

`:.\ text(Value of investment)`	`=5000xx1.34`
	`=$6700`

Financial Maths, STD2 F4 2013 HSC 26e

Kimberley has invested $3500.

Interest is compounded half-yearly at a rate of 2% per half-year.

Use the table to calculate the value of her investment at the end of 4 years. (2 marks)

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`$4102`

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♦ Mean mark 44%
COMMENT: Structure your answer: 1-Find the interest rate per compounding period (same in this case). 2-Find the number of compounding periods.

`r =\ text(2% per half-year)`

`n = 8 \ \ \ \ text{(8 half-years in 4 years)}`

`=>\ text(Table Factor = 1.172)`

`text(Investment)`	`= 3500` ` xx 1.172`
	`= $4102`

`:.\ text(After 4 years, investment value is $4102)`

Financial Maths, STD2 F4 2012 HSC 9 MC

Tracy invests some money for 2 years at 4% per annum, compounded quarterly.

Which figure from the table should Tracy use to calculate the value of her investment at the end of 2 years?

1.020
1.082
1.083
1.369

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`C`

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♦♦♦ Mean mark 24%. The lowest MC mean mark in the 2012 exam.
COMMENT: A process to follow: 1-convert the annual rate to the rate per compounding period. 2-calculate the number of compounding periods.

`text(4% annual)`

`=>\ text(4%)/4=text(1% compounded each quarter)`

`=>n=8\ \ \ \ \ \ text{(8 quarters in 2 years)}`

`:.\ text{Factor = 1.083 (from table)}`

`=> C`