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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?

  1. 21 000 × 1.0816
  2. 21 000 ÷ 1.0816
  3. 21 000 × 1.0829
  4. 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.
 

2ug-2016-hsc-8-mc 

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

  1.    $1124.86
  2.    $2812.15
  3.    $3624.86
  4.    $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.

2UG 2011 23c

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.

2013 26e

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. 

2012 9 mc

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

  1.   1.020 
  2.   1.082
  3.   1.083
  4.   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`