Classroom · Years 9–10
Where does interest on interest come from?
Start with $1,000. Add 5% interest each year. Will three years give you $150 interest, or more? Find out one year at a time.
1. Predict, then investigate
| Period | Opening ($) | Interest ($) | Closing ($) |
|---|
Arithmetic is carried without intermediate rounding; displayed amounts are rounded to cents. $ denotes illustrative dollars. No tax, fees, inflation or changing rates are modelled.
2. From rows to a rule
In the starter, the first year adds $1,000 × 0.05 = $50. The closing balance is $1,050. The second year earns 5% of $1,050, not 5% of the original $1,000.
Adding 5% means keeping 100% and adding 5%: multiply by 1.05. Repeat once for every year:
$1,000 × 1.05 × 1.05 × 1.05 = $1,157.625 → $1,157.63.
For starting balance P, decimal annual rate r and n whole years, A = P(1 + r)n. This lesson compounds once per year. A is the final balance, not the interest alone: interest = A − P.
With simple interest, the same $50 is added each year: $1,000 + 3 × $50 = $1,150. With compound interest, earlier interest also earns interest.
3. Try it without the tool
- Start with $800 at 10% each year. Find the closing balances after years 1, 2 and 3. How much of the final balance is interest?
- A student writes “three years at 5% means multiply by 1.15”. Explain when this is valid, and why it is not the compound-interest rule.
- What happens to the difference between simple and compound interest if the rate is zero? What if there is only one year?
Reveal worked answers
- $880, $968 and $1,064.80. Interest is $1,064.80 − $800 = $264.80.
- Multiplying by 1.15 gives three years of simple interest at 5% on the original balance. Compound interest multiplies by 1.05 three times: 1.157625.
- At 0%, neither model earns interest. Over one year both use the same opening balance, so their results agree.
Teaching notes and next steps
Ask students to name the amount on which each year’s interest is calculated. A useful misconception to discuss is confusing $157.63 interest with the $1,157.63 balance.
Designed around NSW Stage 5 MA5-FIN-C-02, Financial Mathematics B: repeated calculations, repeated multiplication and simple/compound comparisons. This is an independent resource, not a NESA-endorsed lesson.
Next: investigate growth and depreciation. For additional frequencies, use the compound interest formula guide or full simple versus compound calculator.