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.

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

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Determine the value that belongs in cell C9. (1 mark)
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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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Show Answers Only

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

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

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

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

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

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

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

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

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

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

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