Financial Maths, STD2 EO-Bank 29

Dao takes out a reducing balance loan of $5000. The loan has an interest rate of 12% per annum, compounded monthly, and Dao makes monthly repayments of $900.

The spreadsheet shown models the first 4 months of the loan.

Calculate the value in cell C9. (1 mark)
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By continuing the spreadsheet, determine the number of months it takes Dao to repay the loan in full, and calculate the value of the final repayment. (3 marks)
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Show Answers Only

a. $\text{C9} = \$41.50$

b. $\text{The loan is repaid in}\ 6\ \text{months.}$

$\text{Final repayment} = \$670.78$

Show Worked Solution

a. $\text{Monthly interest rate} = \dfrac{12\%}{12} = 1\%$

$\text{C9 (Month 2 interest)} = 4150 \times 0.01 = \$41.50$

b. $\text{Continue the schedule using}\ \ P+I-R\ \ \text{each month:}$

$\text{Month 5:}\ 1548.65+1548.65 \times 0.01-900=\$664.14$

$\text{Month 6:}\ 664.14+664.14 \times 0.01=\$670.78$

$\text{The Month 6 balance owing}\ (\$670.78)\ \text{is less than the}$

$\text{usual}\ \$900\ \text{repayment, so this final repayment clears the loan.}$

$\therefore\ \text{The loan is repaid in}\ 6\ \text{months, with a final}$

$\text{repayment of}\ \$670.78.$