Inflation/tax/fees | Year 12

01 / LEARN

The idea, step by step

Apply deductions to the right quantity

If tax is charged only on interest, it is the interest—not the entire account balance—that is multiplied by the tax fraction. With interest rate r and tax fraction t, an after-tax interest rate is r(1−t), when tax is deducted at each period end.

A percentage account fee must have a specified base and timing. A fixed dollar fee is a cash flow, so subtract it in the recurrence rather than subtracting its number from the rate. Apply each operation in the stated order.

Purchasing power compares two growth factors

A balance can increase while its purchasing power falls. Divide its nominal growth factor by the price growth factor. For one year with a nominal net return r and inflation f, the exact real return is $(1 + r) / (1 + f) - 1$ .

Subtracting inflation from the return is an approximation, not the exact formula. To express a future balance in today’s dollars after n years at constant inflation f, divide by ${(1 + f)}^{n}$ . State whether a target is in future dollars or today’s dollars.

r_{r e a l} = \frac{1 + r_{n e t}}{1 + f} - 1

A common trap

Taxing the whole balance or subtracting a fixed dollar fee as though it were a percentage.

Instead: Apply each deduction to its stated base, then follow the timing of the account model.

02 / WORKED EXAMPLES

See the thinking

Example 1

Build the model

AUD 5,000 earns 6% for one year. A stated 20% tax applies only to interest. Find the net interest and final balance.

Gross interest is $5000 \times 0.06 = 300$ .
$T a x = 300 \times 0.20 = 60$ .
Net interest is 240; balance is 5240.

Net interest AUD 240.00; balance AUD 5,240.00.

Example 2

Use the model to make a decision

An investment has a 5% net nominal annual return while prices rise 3%. Find the exact real annual return.

Compare growth factors, not percentage points.
Real factor is $1.05 / 1.03$ .
Subtract 1 to get the rate.

1.9417%

Check your understanding

A 7% annual return is taxed at a stated 25% of interest. Find the after-tax interest rate.

Show answer

5.2500%

The retained fraction of interest is 0.75. Net rate is $0.07 \times 0.75 = 0.0525$ .

03 / WORKSHEET

Your turn

6 questions · 18 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

AUD 8,000 earns 4% interest, then a fixed AUD 50 fee is charged. Find the final balance.
3 marks
A 7% annual return is taxed at a stated 25% of interest. Find the after-tax interest rate.
3 marks
Prices rise 2.5% annually for 4 years. What future amount has the purchasing power of AUD 10,000 today?
3 marks
A balance of AUD 15,000 in 5 years is measured when inflation has been 3% annually. Express it in today’s dollars.
3 marks
An account grows 2% while prices grow 4%. Calculate its real return and interpret the sign.
3 marks
AUD 3,000 earns 5%, then a fee of 1% of the post-interest balance is charged. Find the final balance.
3 marks

Read the worked solutions

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

AUD 8,000 earns 4% interest, then a fixed AUD 50 fee is charged. Find the final balance.
3 marks
Interest is $8000 \times 0.04 = 320$ .
Balance is $8000 + 320 - 50 = 8270$ .
AUD 8,270.00
A 7% annual return is taxed at a stated 25% of interest. Find the after-tax interest rate.
3 marks
The retained fraction of interest is 0.75.
Net rate is $0.07 \times 0.75 = 0.0525$ .
5.2500%
Prices rise 2.5% annually for 4 years. What future amount has the purchasing power of AUD 10,000 today?
3 marks
Increase the target by the price growth factor.
Future target is $10000 {(1.025)}^{4}$ .
AUD 11,038.13
A balance of AUD 15,000 in 5 years is measured when inflation has been 3% annually. Express it in today’s dollars.
3 marks
Discount the future dollars by cumulative inflation.
Real amount is $15000 / {(1.03)}^{5}$ .
AUD 12,939.13
An account grows 2% while prices grow 4%. Calculate its real return and interpret the sign.
3 marks
Real factor is $1.02 / 1.04$ .
The result is below 1, so the real rate is negative.
-1.9231%; purchasing power falls.
AUD 3,000 earns 5%, then a fee of 1% of the post-interest balance is charged. Find the final balance.
3 marks
Post-interest balance is $3000 \times 1.05 = 3150$ .
Retain 99% after the stated fee: $3150 \times 0.99 = 3118.50$ .
AUD 3,118.50

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 2 General Mathematics financial models: investments and annuities, superannuation, income streams and borrowing. Original practice uses supplied hypothetical rates, taxes and fees; statutory or commercial conditions are not inferred.

Official curriculum source ↗

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