Tax/inflation effects on returns | Year 11

01 / LEARN

Understand the idea.

Apply the stated tax rule

Apply the tax rule to the amount it actually names. In this simplified model, only interest is taxed: if interest is $I$ and the supplied tax fraction is $t$ , tax is $I t$ and retained interest is $I (1 - t)$ . The original principal remains in the account.

Timing changes future growth. Tax deducted from each interest credit reduces the balance available to earn later interest; a single deduction at the end is a different model. Follow the stated convention instead of treating all tax deductions as interchangeable.

Adjust for inflation

Inflation changes what a monetary balance can buy. To convert a future amount to starting-year purchasing power, divide it by the price-level growth factor. After one year, an after-tax money growth factor $1 + r$ becomes a real factor $\frac{1 + r}{1 + f}$ when inflation is $f$ .

Subtract 1 from the real factor to find the real rate. Subtracting inflation directly from the nominal rate is only an approximation. A balance can rise in dollars while falling in purchasing power if prices grow by a larger proportional amount.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

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.

Worked solution

1
Calculate the gross interest.
$I = 10 000 (0.06) = AUD 600$
The 6% interest rate applies to the original AUD 10000 for the stated year.
2
Apply tax only to the interest.
$T = 600 (0.30) = AUD 180$
The supplied 30% tax rule uses AUD 600 as its reference, rather than the principal.
3
Find the retained interest.
$I_{net} = 600 - 180 = AUD 420$
Retained interest is the gross interest left after its tax deduction.
4
Find the closing balance.
$B = 10 000 + 420 = AUD 10 420$
The principal is unchanged by the interest-only tax rule.

Answer

AUD 180 tax; AUD 420 retained; AUD 10420 balance

EXAMPLE 02

Worked example

Use that AUD 10420 balance with 2.5% inflation. Find its value in starting-year dollars and real return.

Worked solution

1
Write the price-level factor.
$G_{prices} = 1 + 0.025 = 1.025$
Prices are 102.5% of their starting level after 2.5% inflation.
2
Convert the balance to starting-year purchasing power.
$V = \frac{10 420}{1.025} \approx AUD 10 165.85$
Dividing by the price factor expresses the future balance in starting-year dollars.
3
Compare the purchasing value with the original deposit.
$r_{real} = \frac{1.042}{1.025} - 1 \approx 0.016585366$
The money balance grew by 4.2% after tax; the real comparison also accounts for the higher price level.
4
State the real percentage return.
$r_{real} \approx 1.659 %$
Convert the decimal gain to a percentage and round to three decimal places.

Answer

AUD 10,165.85; 1.659%

03 / YOUR TURN

Try it yourself.

Check your understanding

A model pays AUD 200 interest and taxes it at 25%. How much is retained?

Show answer & reasoning

AUD 150.00

The tax is $200 (0.25) = AUD 50$ . Retained interest is $200 - 50 = AUD 150.00$ , equivalently $200 (0.75)$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

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
$0.05 \times 0.70 = 0.035$ .
3.5%
A balance grows 7% while prices rise 4%. Find the exact real growth rate to 3 decimal places.
2 marks
$Real factor = \frac{1.07}{1.04}$ .
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
$\frac{6000}{1.02}$ .
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
$Real rate = \frac{1.03}{1.05} - 1 < 0$ .
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.

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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 ↗

In this lesson

Understand the idea.

Apply the stated tax rule

Adjust for inflation

See the method in action.

Worked example

Calculate the gross interest.

Apply tax only to the interest.

Find the retained interest.

Find the closing balance.

Worked example

Write the price-level factor.

Convert the balance to starting-year purchasing power.

Compare the purchasing value with the original deposit.

State the real percentage return.

Try it yourself.

Check your understanding

Keep practising