Modelling and checking financial problems with digital tools | Year 8

01 / LEARN

Understand the idea.

Build a transparent model

A financial model links quantities with a stated rule. For weekly saving, closing balance equals opening balance plus income minus spending. Record assumptions such as fixed weekly amounts and no fees or interest, so the prediction can be interpreted correctly.

With opening balance in B, income in C, spending in D and closing balance in E, enter $=B2+C2-D2$ in E2. The next opening balance can use $=E2$ . When copying formulas, check that row references update as intended.

Weekly savings model: all amounts in AUD
Week	Opening balance	Income	Spending	Closing balance
1	240	30	18	252
2	252	30	18	264
3	264	30	18	276
4	276	30	18	288

Check and vary the model

Check a row by hand, then check the overall pattern by a second method. A fixed weekly net gain gives $balance = start + weeks \times net gain$ . Changing income or spending should change the prediction in the expected direction.

For simple interest, use $I = P r t$ , where $P$ is principal, $r$ is the yearly rate as a decimal and $t$ is time in years. Interest is calculated on the original principal, with a fixed rate and fees handled separately.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Check a savings spreadsheet

A balance starts at 240 AUD, with 30 AUD received and 18 AUD spent each week. Find the balance after four weeks.

Worked solution

1
Find the net weekly gain.
$30 - 18 = 12 AUD$
Income raises the balance and spending lowers it during each week.
2
Find the gain over four weeks.
$4 \times 12 = 48 AUD$
The same net amount is added once per week under the fixed-amount model.
3
Add the gain to the starting balance.
$240 + 48 = 288 AUD$
The final balance includes the original savings as well as the four weekly gains.
4
Check the repeated pattern.
$\begin{aligned} 240 + 12 & = 252 \\ 252 + 12 & = 264 \\ 264 + 12 & = 276 \\ 276 + 12 & = 288 \end{aligned}$
Successive weekly closing balances agree with the direct four-week calculation.

Answer

288 AUD

EXAMPLE 02

Test an interest rule

A classroom model pays simple interest on 500 AUD at 4% per year for two years. Find interest and final balance.

Worked solution

1
Convert the annual percentage rate.
$4 % = \frac{4}{100} = 0.04$
The simple-interest formula uses the rate as a decimal per year.
2
Calculate simple interest.
$I = P r t = 500 \times 0.04 \times 2 = 40 AUD$
Each year earns interest on the original five hundred dollars, with no interest on earlier interest.
3
Find the final balance.
$500 + 40 = 540 AUD$
The model adds the total interest to the principal and includes no fees or withdrawals.

Answer

40 AUD interest; 540 AUD final balance.

03 / YOUR TURN

Try it yourself.

Check your understanding

A saving model starts at 100 AUD and adds a net 8 AUD per week. What balance should its third row show after three weeks?

Show answer & reasoning

124 AUD

Three complete weeks add $3 \times 8 = 24 AUD$ to the initial balance, giving $100 + 24 = 124 AUD$ . The first completed week is counted after, not before, the starting balance.

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

A savings model starts at 80 AUD. Weekly income is 15 AUD and spending is 9 AUD. Find the balance after five weeks.
2 marks
Columns B, C and D contain opening balance, income and spending. Write a spreadsheet formula for closing balance E2.
2 marks
A row has $B2 = 200$ , $C2 = 25$ and $D2 = 17$ . A formula displays 242. Check the row and give the correct closing balance.
2 marks
Compare two alternative six-week plans, each starting with 150 AUD. In Plan A, the net weekly gain is 10 AUD. In Plan B, weekly spending is 4 AUD higher than in Plan A while income is unchanged. Find the balance after six weeks under each plan.
3 marks
Use a simple-interest model for 300 AUD at 5% per year for three years. Find interest and final balance.
2 marks
A model predicts a 400 AUD balance after saving 20 AUD weekly for ten weeks from a 200 AUD start. State two assumptions and explain how an unplanned 35 AUD expense changes the prediction.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A savings model starts at 80 AUD. Weekly income is 15 AUD and spending is 9 AUD. Find the balance after five weeks.
2 marks
Net change: $15 - 9 = 6$ AUD per week.
$80 + 5 \times 6 = 110$ .
110 AUD
Columns B, C and D contain opening balance, income and spending. Write a spreadsheet formula for closing balance E2.
2 marks
Add income to opening balance and subtract spending.
$=B2+C2-D2$
A row has $B2 = 200$ , $C2 = 25$ and $D2 = 17$ . A formula displays 242. Check the row and give the correct closing balance.
2 marks
$200 + 25 - 17 = 208$ .
The displayed 242 does not fit the intended rule.
208 AUD
Compare two alternative six-week plans, each starting with 150 AUD. In Plan A, the net weekly gain is 10 AUD. In Plan B, weekly spending is 4 AUD higher than in Plan A while income is unchanged. Find the balance after six weeks under each plan.
3 marks
Original: $150 + 6 \times 10 = 210$ .
New net gain: $10 - 4 = 6$ AUD.
Changed: $150 + 6 \times 6 = 186$ .
Original: 210 AUD; changed spending: 186 AUD.
Use a simple-interest model for 300 AUD at 5% per year for three years. Find interest and final balance.
2 marks
Interest: $300 \times 0.05 \times 3 = 45$ .
Balance: $300 + 45 = 345$ .
45 AUD interest; 345 AUD balance.
A model predicts a 400 AUD balance after saving 20 AUD weekly for ten weeks from a 200 AUD start. State two assumptions and explain how an unplanned 35 AUD expense changes the prediction.
3 marks
Original: $200 + 10 \times 20 = 400$ .
Subtract the extra expense: $400 - 35 = 365$ .
Other valid assumptions include timing, fixed income or no interest; the model must match its stated rules.
Assume net weekly saving stays 20 AUD and no fees/other changes; the revised prediction is 365 AUD.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Percentage increase/decrease; finding an original amount; discounts and mark-ups; percentage comparisons; budgets and purchase decisions; modelling and checking financial problems with digital tools. Simple interest can be offered here as a school-dependent application and developed in Year 9.

Official curriculum source ↗

In this lesson

Understand the idea.

Build a transparent model

Check and vary the model

See the method in action.

Check a savings spreadsheet

Find the net weekly gain.

Find the gain over four weeks.

Add the gain to the starting balance.

Check the repeated pattern.

Test an interest rule

Convert the annual percentage rate.

Calculate simple interest.

Find the final balance.

Try it yourself.

Check your understanding

Keep practising