Modelling and checking financial problems with digital tools | Year 8

01 / LEARN

The idea, step by step

Build a transparent model

A financial model links quantities with a rule. In a savings plan, closing balance equals opening balance plus income minus spending. Write the assumptions beside the table: for example, weekly income and spending stay fixed, and no account fees or interest apply.

With columns B = opening balance, C = income, D = spending and E = closing balance, the first spreadsheet rule could be =B2+C2-D2. The next row can use =E2 as its opening balance. The cell references matter: copying a rule should update to the intended row.

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 the first row by hand and compare the pattern with the story. In the table, the weekly gain is $30 - 18 = 12$ AUD, so after four weeks the balance is $240 + 4 \times 12 = 288$ AUD. This second method checks the repeated formulas.

Then change one assumption. If weekly spending rises, the model should predict less saving. A simple-interest illustration uses interest = principal Ã— yearly rate Ã— number of years, with the rate written as a decimal; this assumes interest is not added to the amount earning interest. It is an introductory financial model, not a promise about actual accounts.

A common trap

A spreadsheet output is correct just because it displays a number.

Instead: Check the rule, units, cell references and assumptions, then verify at least one row by hand.

02 / WORKED EXAMPLES

See the thinking

Example 1

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.

The net weekly change is $30 - 18 = 12$ AUD.
Four weeks add $4 \times 12 = 48$ AUD.
The balance is $240 + 48 = 288$ AUD, matching the supplied table.

288 AUD

Example 2

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.

Write 4% as 0.04.
Interest: $500 \times 0.04 \times 2 = 40$ AUD.
Final balance: $500 + 40 = 540$ AUD. The model assumes the rate stays fixed and there are no fees.

40 AUD interest; 540 AUD final balance.

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

124 AUD

$100 + 3 \times 8 = 124$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF 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…

Ready for the topic test?

Review the chapter, then choose a practice test.

Topic review

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 ↗

Back to Percentages and financial mathematics