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Financial Maths, STD1 F2 2024 HSC 28

Alex and Jun each invest $1800 for 5 years.

    • Alex's investment earns simple interest at a rate of 7.5% per annum.
    • Jun's investment earns interest at a rate of 6.0% per annum, compounding quarterly.

By calculating the interest earned over the 5 years, determine who will have the greater amount.   (3 marks)

Show Answers Only

\(\text {Alex’s investment:}\)

\(\text{Interest}=Prn=1800 \times 0.075 \times 5=\$ 675\)
 

\(\text {Jun’s investment:}\)

\(r=\dfrac{6.0\%}{4}=1.5 \% \text { per quarter}\)

\(\text {Compounding periods }=5 \times 4=20\)

\(F V=P V(1+r)^n=1800(1+0.015)^{20}=\$ 2424.34\)

\(\text{Total interest}=F V-P V=2424.34-1800=\$ 624.34\)
 

\(\text {Alex’s interest }>\text { Jun’s interest.}\)

\(\Rightarrow \text{ Alex will have a greater amount (since original investment the same)}\)

Show Worked Solution

\(\text {Alex’s investment:}\)

\(\text{Interest}=Prn=1800 \times 0.075 \times 5=\$ 675\)
 

\(\text {Jun’s investment:}\)

\(r=\dfrac{6.0\%}{4}=1.5 \% \text { per quarter}\)

\(\text {Compounding periods }=5 \times 4=20\)

\(F V=P V(1+r)^n=1800(1+0.015)^{20}=\$ 2424.34\)

\(\text{Total interest}=F V-P V=2424.34-1800=\$ 624.34\)
 

\(\text {Alex’s interest }>\text { Jun’s interest.}\)

\(\Rightarrow \text{ Alex will have a greater amount (since original investment the same)}\)

Financial Maths, STD1 F2 2022 HSC 24

Peta has the choice of investing $7000 in two different investment funds.

Fund A:  5.2% per annum simple interest

Fund B: 5% per annum interest, compounded annually

What is the difference between the amounts of interest earned in the two investment funds over 3 years?  (4 marks)

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`$11.38`

Show Worked Solution

`text{Fund A}`:

`text{Simple Interest}`  `= 7000xx 5.2text{%}xx 3`  
  `= 7000xx 0.052xx 3`  
  `= $1092`  

   
`text{Fund B}`:

`FV` `=PV (1+r)^n`  
  `= 7000 (1+0.05)^3`  
  `=$8103.38\ \ text{(nearest cent)}`  

 

`text{Interest}` `= FV-PV`  
  `=8103.38-7000`  
  ` = $1103.38`  

  

`:.\ text{Difference}` `= 1103.38-1092`  
  `=$11.38`  

♦ Mean mark 44%.

 

Financial Maths, STD1 F2 2021 HSC 9 MC

James invests $5000 at 3% per annum simple interest for 2 years, while Sally invests $5000 at 3% per annum compounded annually for 2 years.

For the given investments, which of the following statements is TRUE?

  1. James earns more interest than Sally.
  2. Sally earns more interest than James.
  3. James and Sally earn the same amount of interest.
  4. There is not enough information to compare the interest earned by James and Sally.
Show Answers Only

`B`

Show Worked Solution

`text{Investments earn more when interest is compounded (vs simple}`

`text{interest) because interest is paid on both the principal and earlier}`

`text{interest.}`

`:.\ text(Sally earns more interest than James.)`

`=> B`

Financial Maths, STD1 F2 2020 HSC 25

Tom is offered two different investment options.

Option A: 10% per annum simple interest.

Option B: 9% per annum interest, compounded annually.

Tom has $1000 to invest. The graph shows the future values over time of $1000 invested using Option B.
 


 

Tom wants to find the difference between the future values after 8 years using these two investment options.

By first drawing, on the grid above, the graph of the future values of $1000 invested using Option A, estimate the difference between the future values after 8 years.   (3 marks)

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`$200`

Show Worked Solution

♦♦ Mean mark 30%.

`text{When}\ \ t = 8 \ text{years:}`

`text{Option} \ A = $1800 \ , \ text{Option} \ B = $2000`

`therefore \ text{Estimate of difference}` `= 2000 – 1800`
  `= $ 200`

Financial Maths, STD1 F2 2019 HSC 35

A bank offers two different savings accounts.

Account `X` offers simple interest of 7% per annum.
Account `Y` offers compound interest of 6% per annum compounded yearly.

The table displays the future values of $20 000 invested in each account for the first 2 years.
 


  

  1. How much more money is there in Account `X` than in Account `Y` at the end of 2 years?  (1 mark)

  2. Show that there would be more money in Account `Y` than in Account `X` at the end of 8 years.  (3 marks)

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  1. `$328`
  2. `text(See Worked Solutions)`
Show Worked Solution
a.    `text(Extra money in)\ \ X` `= 22\ 800 – 22\ 472`
    `= $328`

 

b.   `text(Account)\ X:`

♦ Mean mark part (b) 30%.

`I` `= Prn`
  `= 20\ 000 xx 7/100 xx 8`
  `= 11\ 200`

 
`=> text(Balance)\ X = 20\ 000 + 11\ 200 = $31\ 200`
 

`text(Account)\ Y:`

`FV` `= PV(1 + r)^n`
  `= 20\ 000(1 + 6/100)^8`
  `= $31\ 876.96`

 
`:. text(After 8 years, there’s more money in Account)\ Y.`

Financial Maths, STD2 F1 2007 HSC 23a

Lilly and Rose each have money to invest and choose different investment accounts.

The graph shows the values of their investments over time.
 

 

  1. How much was Rose’s original investment?  (1 mark)

  2. At the end of  6 years, which investment will be worth the most and by how much?  (2 marks)

  3. Lilly’s investment will reach a value of  $20 000  first.
  4. How much longer will it take Rose’s investment to reach a value of  $20 000?   (1 mark)

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  1. `$5000`
  2. `text(Rose’s is worth $2000 more.)`
  3. `text(It takes Lilly 14 years to reach $20 000 and it takes)`

     

    `text{Rose 1 year longer (15 years) to reach the same value}`

Show Worked Solution

i.  `$5000\ text{(} y text(-intercept) text{)}`
 

ii.  `text(After 6 years,)`

`text(Lilly’s investment)` `= $9000`
`text(Rose’s investment)` `= $11\ 000`
`:.\ text(Rose’s is worth $2000 more.)`

  

iii.  `text(It takes Lilly 14 years to reach $20 000 and it)`

`text{takes Rose 1 year longer (15 years) to reach the}`

`text(same value.)`