The idea, step by step
Apply the stated tax rule
This lesson uses a simplified flat tax on interest only; it is not a calculation of anyone’s actual tax liability. If interest is and the supplied tax fraction is , tax is and retained interest is . The principal is not taxed in this model.
If tax is deducted after each interest credit, later growth uses the after-tax credit. If it is deducted only once at the end, use that different timing. The question must specify the convention.
Adjust for inflation
Inflation describes a rise in prices in the model. To express a future balance in starting-year purchasing power, divide it by the price-level factor. After one year with net nominal growth and inflation , the exact real rate is .
Subtracting inflation from nominal return is a useful rough estimate for small rates, but it is not the exact compound relation. A positive money return can coincide with a loss of purchasing power.
A common trap
Subtract the tax percentage from the interest percentage.
Instead: Tax applies to the interest amount in this simplified model. A 6% rate taxed at 30% leaves 6%×0.70=4.2%, not −24%.
See the thinking
Worked example
AUD 10000 earns 6% interest. A supplied 30% flat tax applies only to interest at year end. Find tax, retained interest and balance.
- Gross interest=600.
- Tax=600×0.30=180.
- Retained=420;balance=10420.
Worked example
Use that AUD 10420 balance with 2.5% inflation. Find its value in starting-year dollars and real return.
- Starting-year purchasing value=10420/1.025.
- Real rate=1.042/1.025−1=0.0165854.
Check your understanding
A model pays AUD 200 interest and taxes it at 25%. How much is retained?
Show answer
AUD 150.00
200(1−0.25)=150.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- AUD 5000 earns 4% interest. Tax is 20% of the interest. Find tax and retained earnings.2 marks
- What after-tax rate results from 5% interest taxed at 30% of each interest credit?2 marks
- A balance grows 7% while prices rise 4%. Find the exact real growth rate to 3 decimal places.2 marks
- AUD 6000 in one year has prices 2% higher. Express it in current-year purchasing power.2 marks
- An investment grows 3% after tax while inflation is 5%. Is purchasing power higher or lower? Quantify to 3 decimal places.2 marks
- Why does the formula not describe actual tax on every possible investment?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- AUD 5000 earns 4% interest. Tax is 20% of the interest. Find tax and retained earnings.2 marks
Interest=200.
Tax=40;retained=160.
AUD 40 tax; AUD 160 retained - What after-tax rate results from 5% interest taxed at 30% of each interest credit?2 marks
0.05×0.70=0.035.
3.5% - A balance grows 7% while prices rise 4%. Find the exact real growth rate to 3 decimal places.2 marks
Real factor=1.07/1.04.
Subtract 1 and express as a percentage.
2.885% - AUD 6000 in one year has prices 2% higher. Express it in current-year purchasing power.2 marks
6000/1.02.
AUD 5,882.35 - An investment grows 3% after tax while inflation is 5%. Is purchasing power higher or lower? Quantify to 3 decimal places.2 marks
Real rate=1.03/1.05−1<0.
Lower by 1.905% - Why does the formula not describe actual tax on every possible investment?2 marks
The problem supplies a simplified rule; the conclusion is limited to that model.
Tax rules differ across types of income, personal circumstances and timing.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.
Official curriculum source ↗