Financial Maths, STD2 EO-Bank 28

Talia takes out a reducing balance loan of $12 000 to buy a boat. The loan has an interest rate of 7.2% per annum and Talia makes monthly repayments of $300.

The spreadsheet shown models the first 3 months of the loan.

Calculate the value in cell C9. (1 mark)
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From the end of month 3, Talia increases her monthly repayment from $300 to $500. Calculate the balance owing at the end of month 6, and determine how much less Talia owes compared to keeping repayments at $300. (3 marks)
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a. $\text{C9} = \$70.63$

b. $\text{Balance at end of month 6} = \$10\,007.71$

$\text{Talia owes}\ \$603.61\ \text{less than at the standard repayment.}$

Show Worked Solution

a. $\text{Monthly interest rate} = \dfrac{7.2\%}{12} = 0.6\%$

$\text{C9 (Month 2 interest)} = 11\,772 \times 0.006 = \$70.63$

b. $\text{Using}\ \ P+I-R\ \ \text{from end of month 3 balance}\ \$11\,311.89:$

$\text{Increased repayments of}\ \$500\ \text{from month 4:}$

$\text{Month 4:}\ 11\,311.89+11\,311.89 \times 0.006-500=\$10\,879.76$

$\text{Month 5:}\ 10\,879.76+10\,879.76 \times 0.006-500=\$10\,445.04$

$\text{Month 6:}\ 10\,445.04+10\,445.04 \times 0.006-500=\$10\,007.71$

$\text{Standard repayments of}\ \$300\ \text{from month 4:}$

$\text{Month 4:}\ 11\,311.89+11\,311.89\times 0.006-300=\$11\,079.76$

$\text{Month 5:}\ 11\,079.76+11\,079.76\times 0.006-300=\$10\,846.24$

$\text{Month 6:}\ 10\,846.24+10\,846.24\times 0.006-300=\$10\,611.32$

$\text{Difference}=10\,611.32-10\,007.71=\$603.61$

$\therefore\ \text{Talia owes}\ \$603.61\ \text{less by increasing her repayments.}$