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Financial Maths, STD2 2024 HSC 20 (Adapted)

A table of future value interest factors for an annuity of $1 is shown.

  
 

  1. Callum invests $300 at the end of each year for 6 years into an account earning 4% per annum, compounded annually. Using the table, calculate the future value of Callum’s investment.   (1 mark)
  2. Devi wants to have saved $6200 in 4 years. She will make equal payments at the end of every six months into an account paying 6% per annum, compounded six-monthly.
  3. Using the table, find the minimum amount Devi must pay each six months. Give your answer to the nearest $10 and support it with calculations.   (2 marks)
Show Answers Only

a.    \(\$1989.90\)

b.    \($700\ \text{(nearest \$10)}\)

Show Worked Solution

a.    \(\text{6 annual periods at 4% p.a.}\Rightarrow\text{Factor}=6.6330\)

\(FV=300\times 6.6330=\$1989.90\)
  

b.    \(r=\dfrac{6\%}{2}=3\%\ \text{per 6 months}\)

\(\text{Compounding periods}=4\times 2=8\)

\(\Rightarrow\ \text{Factor}=8.8923\)
 

\(\text{Find minimum payment:}\)

\(6200\) \(=\text{Payment}\times 8.8923\)
\(\text{Payment}\) \(=\dfrac{6200}{8.8923}=697.23\ldots=$700\ \text{(nearest \$10)}\)