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Financial Maths, STD2 2025 HSC 34 (Adapted)

The table shows future value interest factors for an annuity of $1.
   

Larry invests a single amount of $18 000 for 5 years at 9% per annum, compounding monthly.

Tobias wants to end up with the same amount as Larry by using an annuity. He will pay a fixed sum into an account at the end of each month for 5 years, with the account also paying 9% per annum, compounding monthly.

Using the table, work out how much Tobias must deposit each month.   (3 marks)

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\(\$373.65\)

Show Worked Solution

\(r=\dfrac{0.09}{12}=0.0075,\ \ n=12\times 5=60\)

\(\text{Larry’s investment:}\)

\(FV=18\,000(1+0.0075)^{60}=28\,182.26\)
  

\(\text{Tobias’s investment:}\)

\(\text{Annuity factor:}\ 75.42414\)

\(\text{Annuity}\times 75.42414\) \(=\$28\,182.26\)
\(\text{Annuity}\) \(=\dfrac{28\,182.26}{75.42414}=\$373.65\)

Financial Maths, STD2 2021 HSC 31 (Adapted)

Present value interest factors for an annuity of $1 for various interest rates \((r)\) and numbers of periods \((N)\) are given in the table.

  
 

A bank lends Paula $600 000 to buy an apartment, with interest charged at 1.8% per annum compounding monthly. She agrees to repay the loan in equal monthly repayments over a 25-year period.

What monthly repayment is needed to repay the loan in 25 years? Give your answer correct to the nearest cent.   (2 marks)

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\(\text{Monthly repayment}=\$2485.11\)

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\(\text{Monthly interest rate}\ (r)=\dfrac{1.8}{12}\%=0.15\%=0.0015\)

\(N=25\times 12=300\)

\(\Rightarrow\ \text{PV annuity factor}=241.43789\)
 

\(\therefore\ \text{Monthly repayment}=\dfrac{600\,000}{241.43789}=\$2485.11\)

Financial Maths, STD2 2023 HSC 25 (Adapted)

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

  
 

  1. Sue wants to save $180 000 over the next 5 years. The account pays 8% per annum, compounding annually.
  2. Using the table, find the amount Sue should contribute each year, to the nearest dollar.   (2 marks)
  3. Instead, Sue decides to contribute $7500 every three months for 5 years into an account paying 8% per annum, compounding quarterly.
  4. Using the table, find how much Sue will have at the end of 5 years.   (3 marks)
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a.    \(\$30\,680\)

b.    \(\$182\,227.50\)

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a.    \(\text{Applicable interest rate}=8\%\)

\(\text{Compounding periods}=5\times 1=5\)

\(\Rightarrow\ \text{Factor}=5.867\)

\(\therefore\ \text{Contribution (annual)}=\dfrac{180\,000}{5.867}=\$30\,680\ \text{(nearest dollar)}\)
 

b.    \(\text{Applicable interest rate}=\dfrac{8\%}{4}=2\%\ \text{per quarter}\)

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

\(\Rightarrow\ \text{Factor}=24.297\)

\(\therefore\ \text{Total (after 5 years)}=7500\times 24.297=\$182\,227.50\)

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

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

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

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

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