Financial Maths, STD2 EQ-Bank 32

Patricia borrows $20 000 as a reducing balance loan at an interest rate of 6% per annum. She is comparing two repayment options, each repaying the loan over 2 years.

Option A: equal monthly repayments
Option B: equal quarterly repayments

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

Using the table, calculate Patricia's repayment under each option. (2 marks)
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Determine which option costs less in total interest, and by how much. (3 marks)
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Show Answers Only

a. $\text{Monthly} = \$886.41,\ \ \text{Quarterly} = \$2671.69$

b. $\text{Monthly repayments cost}\ \$99.68\ \text{less in interest.}$

Show Worked Solution

a. $\text{Monthly interest rate} = \dfrac{6}{12 \times 100}\ \ \Rightarrow\ \ r=0.005$

$\text{Quarterly interest rate} = \dfrac{6}{4 \times 100}\ \ \Rightarrow\ \ r=0.015$

$\text{Using Repayment} = \dfrac{\text{loan amount}}{\text{PV factor}}:$

$\text{Monthly repayment}= \dfrac{20\,000}{22.5629} = \$886.41$

$\text{Quarterly repayment}= \dfrac{20\,000}{7.4859} = \$2671.69$

b. $\text{Total paid} = \text{repayment} \times \text{number of repayments}$

$\text{Monthly:}\ 886.41 \times 24 = \$21\,273.84$

$\text{Quarterly:}\ 2671.69 \times 8 = \$21\,373.52$

$\text{Interest (monthly)} = 21\,273.84-20\,000 = \$1273.84$

$\text{Interest (quarterly)} = 21\,373.52-20\,000 = \$1373.52$

$\text{Difference} = 1373.52-1273.84 = \$99.68$

$\therefore\ \text{Monthly repayments cost}\ \$99.68\ \text{less in interest.}$