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Financial Maths, STD2 2021 HSC 21 (Adapted)

Trevor opens a savings account with $8000. The account pays interest at a fixed monthly rate. At the end of each month the interest is added, and Trevor then deposits a further $400.

The spreadsheet below records the first six months of the account, together with the start of the seventh month.

 

By first finding the monthly interest rate, complete the row for month 7.   (3 marks)

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\(\text{Monthly rate}=0.2\%\)

\(\text{Month 7: beginning}=\$10\,508.52,\ \text{interest}=\$21.02,\ \text{end}=\$10\,929.54\)

Show Worked Solution

\(\text{Monthly interest rate}=\dfrac{16.00}{8000}=0.002=0.2\%\)

\(\text{Row 7 calculations:}\)

\(\text{Beginning balance}=\$10\,508.52\)

\(\text{Monthly interest}=10\,508.52\times 0.002=\$21.02\)

\(\text{End of month balance}\) \(=10\,508.52+21.02+400\)
  \(=\$10\,929.54\)

Financial Maths, STD2 EO-Bank 28

Leon opens a superannuation account to build up savings for retirement. At the end of each year he pays in $4000, and the account earns 5% per annum, compounded annually.

The spreadsheet below models the first 4 years of the account.

  
 

  1. Write down the formula used in cell C9, using appropriate grid references.   (1 mark)

  2. Determine the value that belongs in cell C9.   (1 mark)
  3. Starting from the end of year 4, Leon lifts his yearly payment from $4000 to $7000. Find the balance in the account at the end of year 7, and state how much larger this is than if he had stayed with $4000 payments.   (3 marks)
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a.    \(\text{=E8*B3}\)

b.    \(\text{C9}=\$410.00\)

c.    \(\text{Balance at end of year 7}=\$42\,025.54\)

\(\text{Leon has}\ \$9457.50\ \text{more than at the standard contribution.}\)

Show Worked Solution

a.    \(\text{Formula: =E8*B3}\)
 

b.    \(\text{C9 (Year 3 interest)}=\text{balance at start}\times\text{rate}\)

\(\text{C9}=8200\times 0.05=\$410.00\)
  

c.    \(\text{Using}\ \ P+I+C\ \ \text{from end of year 4 balance}\ \$17\,240.50:\)

\(\text{Increased contributions of}\ \$7000\ \text{from year 5:}\)

\(\text{Year 5:}\ 17\,240.50+17\,240.50\times 0.05+7000=\$25\,102.53\)

\(\text{Year 6:}\ 25\,102.53+25\,102.53\times 0.05+7000=\$33\,357.66\)

\(\text{Year 7:}\ 33\,357.66+33\,357.66\times 0.05+7000=\$42\,025.54\)
  

\(\text{Standard contributions of}\ \$4000\ \text{from year 5:}\)

\(\text{Year 5:}\ 17\,240.50+17\,240.50\times 0.05+4000=\$22\,102.53\)

\(\text{Year 6:}\ 22\,102.53+22\,102.53\times 0.05+4000=\$27\,207.66\)

\(\text{Year 7:}\ 27\,207.66+27\,207.66\times 0.05+4000=\$32\,568.04\)
  

\(\text{Difference}=42\,025.54-32\,568.04=\$9457.50\)

\(\therefore\ \text{Leon has}\ \$9457.50\ \text{more by increasing his contributions.}\)