SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Financial Maths, GEN2 2025 VCAA 7

Declan is a filmmaker and content creator.

He has taken out a reducing balance loan to fund a new production.

Interest is calculated monthly and Declan makes monthly repayments.

Three rows of the amortisation table for Declan’s loan are shown below.

\begin{array}{|c|c|c|c|c|}
\hline
\hline \rule{0pt}{2.5ex}\quad \textbf{Payment} \quad & \quad\textbf{Payment} \quad & \quad\textbf{Interest} \quad& \textbf{Principal} & \quad\textbf{Balance}\quad\\
\textbf{number} & \textbf{(\$)}  \rule[-1ex]{0pt}{0pt}& \textbf{(\$)} & \quad\textbf{reduction (\$)} \quad& \textbf{(\$)}\\
\hline \hline \rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0.00 & 0.00 & 0.00 & 850\,000.00 \\
\hline \hline \rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & 15\,730.88 & 2975.00 & 12\,755.88 & 837\,244.12 \\
\hline \hline \rule{0pt}{2.5ex}2 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & 2930.35 & 12\,800.53 & 824\,443.59 \\
\hline
\end{array}

  1. What amount, in dollars, did Declan borrow?   (1 mark)
  2. Why is the interest associated with payment 2 lower than the interest associated with payment 1?   (1 mark)
  3. The interest rate on Declan’s loan is 4.2% per annum, compounding monthly.
  4. Using the values in the table, complete the table below.
  5. Round all values to the nearest cent.   (1 mark)

\begin{array}{|c|c|c|c|c|}
\hline
\hline \rule{0pt}{2.5ex}\quad \textbf{Payment} \quad & \quad\textbf{Payment} \quad & \quad\textbf{Interest} \quad& \textbf{Principal} & \quad\textbf{Balance}\quad\\
\textbf{number} & \textbf{(\$)}  \rule[-1ex]{0pt}{0pt}& \textbf{(\$)} & \quad\textbf{reduction (\$)} \quad& \textbf{(\$)}\\
\hline \hline \rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0.00 & 0.00 & 0.00 & 850\,000.00 \\
\hline \hline \rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & 15\,730.88 & 2975.00 & 12\,755.88 & 837\,244.12 \\
\hline \hline \rule{0pt}{2.5ex}2 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & 2930.35 & 12\,800.53 & 824\,443.59 \\
\hline \hline \rule{0pt}{2.5ex}3 \rule[-1ex]{0pt}{0pt}& 15\,730.88 & & & \\
\hline
\end{array}

  1. The last payment required to fully repay the loan is $15 730.71, correct to the nearest cent.
  2. How many payments of $15 730.88 did Declan make before this final payment?   (1 mark)

Show Answers Only

a.    \(\$ 850\,000\)

b.    \(\text{Interest is lower (payment 2 vs payment 1) because it is based on}\)

\(\text{a reduced balance.}\)

c.    \(\text{Interest}=\dfrac{4.2}{100} \times \dfrac{1}{12} \times 824\, 443.59=\$ 2885.55\)

\(\text{Principal reduction}=15\,730.88-2885.55=\$ 12\,845.33\)

\(\text{Balance}=824\,443.59-12\,845.33=\$811\,598.26\)

d.    \(\text{59 payments made before the final payment.}\)

Show Worked Solution

a.    \(\$ 850\,000\)
 

b.    \(\text{Interest is lower (payment 2 vs payment 1) because it is based on}\)

\(\text{a reduced balance.}\)
 

c.    \(\text{Interest}=\dfrac{4.2}{100} \times \dfrac{1}{12} \times 824\, 443.59=\$ 2885.55\)

\(\text{Principal reduction}=15\,730.88-2885.55=\$ 12\,845.33\)

\(\text{Balance}=824\,443.59-12\,845.33=\$811\,598.26\)

♦ Mean mark (c) 40%.

d.    \(\text{Solve for \(N\) (by CAS):}\)

\(N\) \(=\boldsymbol{59.99 \ldots}\)
\(I(\%)\) \(=4.2\)
\(PV\) \(=850\,000\)
\(PMT\) \(=-15\,730.88\)
\(FV\) \(=0\)
\(PY\) \(=CY=12\)

 
\(\therefore \ \text{59 payments made before the final payment.}\)

♦♦♦ Mean mark (d) 21%.

Financial Maths, GEN1 2019 NHT 21 MC

Yazhen has a reducing balance loan.

Six lines of the amortisation table for Yazhen’s loan are shown below.

The interest rate for Yazhen’s loan increased after one of these six repayments had been made.

The first repayment made at the higher interest rate was repayment number

  1. 15
  2. 16
  3. 17
  4. 18
  5. 19
Show Answers Only

`C`

Show Worked Solution

`text(Interest rate) = text(Interest)/text{Balance (higher row)}`
 

`text(Payment 16:)\ \ \ 343/(34\ 299.50) = 0.0100`

`text(Payment 17:)\ \ \ 403.71/(33\ 642.50) = 0.0120`

`text(Payment 18:)\ \ \ 396.55/(33\ 046.21) = 0.0120`
 

`:.\ text(Payment 17 is the 1st at the higher rate.)`

`=>\ C`

CORE, FUR1 2019 VCAA 20 MC

Consider the following amortisation table for a reducing balance loan.
 


 

The annual interest rate for this loan is 3.6%.

Interest is calculated immediately before each payment.

For this loan, the repayments are made

  1. weekly.
  2. fortnightly
  3. monthly.
  4. quarterly.
  5. yearly
Show Answers Only

`C`

Show Worked Solution

`text(Consider payment #1:)`

`text(Interest rate)` `= 900/(300\ 000)`
  `= 0.3%`

 
`text(S) text(ince annual rate = 3.6%, repayments are monthly.)`

`=>  C`

CORE, FUR1 2018 VCAA 23 MC

Five lines of an amortisation table for a reducing balance loan with monthly repayments are shown below.

The interest rate for this loan changed immediately before repayment number 28.

This change in interest rate is best described as

  1. an increase of 0.24% per annum.
  2. a decrease of 0.024% per annum.
  3. an increase of 0.024% per annum.
  4. a decrease of 0.0024% per annum.
  5. an increase of 0.00024% per annum.
Show Answers Only

`A`

Show Worked Solution

`text(Original interest rate)`

♦♦ Mean mark 29%.

`= 967.08/(230\ 256.78) xx 100`

`= 0.0042`

`= 0.42text(% per month)`
 

`text(New interest rate)`

`= 996.99/(226\ 588.02) xx 100`

`= 0.44text(% per month)`
 

`:.\ text(Change)` `= 0.02text(% per month)`
  `= 0.24text(% per annum)`

`=> A`

CORE, FUR1 2016 VCAA 22 MC

The first three lines of an amortisation table for a reducing balance home loan are shown below.

The interest rate for this home loan is 4.8% per annum compounding monthly.

The loan is to be repaid with monthly payments of $1500.
 

 
The amount of payment number 2 that goes towards reducing the principal of the loan is

  1.  $486
  2.  $502
  3.  $504
  4.  $996
  5.  $998
Show Answers Only

`B`

Show Worked Solution
`text(Interest)` `= 249\ 500 xx (4.8text(%))/12`
  `= 249\ 500 xx 0.048/12`
  `= $998`

 

`:.\ text(Amount that reduces principal)`

`= 1500 – 998`

`= $502`

`=> B`