Start Free
Compound interest is one of the most practical topics in the maths curriculum. It shows up in savings accounts, home loans, credit cards, and investment returns. Understanding how it works gives students a genuine life skill alongside their exam preparation.
This guide explains the concept, walks through the formula, and works through several examples at the Year 10 to Year 11 level.
Simple interest vs compound interest
Before tackling compound interest, it helps to understand how it differs from simple interest.
Simple interest is calculated on the original amount only. If you invest $1,000 at 5% simple interest per year, you earn $50 every year, regardless of how long you leave the money there.
Compound interest is calculated on the original amount plus any interest already earned. So after the first year, you have $1,050. In the second year, the 5% applies to $1,050, giving you $52.50 in interest. In the third year, 5% applies to $1,102.50, and so on. The interest earns interest.
Want interactive help with this topic?
imSteyn guides your child step-by-step through every topic in their Cambridge textbook. Try it free.
Start FreeThis difference seems small at first but grows dramatically over time. That is why compound interest is sometimes called "the most powerful force in mathematics."
The compound interest formula
A = P(1 + r)n
Where:
- A = the final amount (principal plus interest)
- P = the principal (the starting amount)
- r = the interest rate per compounding period (as a decimal)
- n = the number of compounding periods
If you want just the interest earned (not the total amount), subtract the principal: Interest = A - P.
Worked example 1: Annual compounding
You invest $2,000 at 6% per annum compounded annually for 4 years. Find the final amount.
P = 2000, r = 0.06 (6% as a decimal), n = 4
A = 2000 × (1 + 0.06)4
A = 2000 × (1.06)4
A = 2000 × 1.26247...
A = $2,524.95 (rounded to the nearest cent)
The interest earned is $2,524.95 - $2,000 = $524.95.
Compare this to simple interest: 2000 × 0.06 × 4 = $480. Compound interest earned $44.95 more over the same period.
Worked example 2: Monthly compounding
You borrow $10,000 at 8% per annum compounded monthly for 3 years. Find the total amount owed.
When interest compounds monthly, you need to adjust the rate and the number of periods:
- Monthly rate: r = 0.08 / 12 = 0.006667
- Number of months: n = 3 × 12 = 36
A = 10000 × (1 + 0.006667)36
A = 10000 × (1.006667)36
A = 10000 × 1.27024...
A = $12,702.37
The interest owed is $2,702.37. Notice that monthly compounding produces a higher total than annual compounding at the same rate, because interest is added more frequently.
Worked example 3: Finding the interest rate
An investment of $5,000 grows to $6,200 over 3 years with annual compounding. What is the annual interest rate?
A = P(1 + r)n
6200 = 5000 × (1 + r)3
(1 + r)3 = 6200 / 5000 = 1.24
1 + r = 1.24(1/3)
1 + r = 1.0743...
r = 0.0743
The annual interest rate is approximately 7.43%.
To find the cube root, use your calculator's power button: 1.24(1/3) or 1.240.3333.
Worked example 4: Finding the time period
How long will it take for $3,000 to double at 9% per annum compounded annually?
A = P(1 + r)n
6000 = 3000 × (1.09)n
(1.09)n = 2
Using trial and improvement:
(1.09)7 = 1.828 (not enough)
(1.09)8 = 1.993 (almost)
(1.09)9 = 2.172 (too much)
It takes approximately 8 to 9 years. More precisely, using logarithms: n = log(2) / log(1.09) = 8.04 years.
The difference compounding frequency makes
The same interest rate produces different results depending on how often it compounds. Here is $10,000 at 10% per annum for 5 years:
| Compounding | Periods per year | Final amount | Interest earned |
|---|---|---|---|
| Annually | 1 | $16,105.10 | $6,105.10 |
| Quarterly | 4 | $16,386.16 | $6,386.16 |
| Monthly | 12 | $16,453.09 | $6,453.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
More frequent compounding always produces a larger amount, though the difference between monthly and daily is relatively small.
Common mistakes to avoid
- Forgetting to convert the percentage to a decimal. 6% becomes 0.06, not 6. Using 6 in the formula gives absurd results.
- Not adjusting the rate and periods for non-annual compounding. If interest compounds monthly, divide the annual rate by 12 and multiply the years by 12.
- Confusing the total amount (A) with the interest earned. The formula gives you A, which includes the original principal. Subtract P to find just the interest.
- Rounding too early. Keep full decimal values in your working and only round the final answer. Early rounding compounds into larger errors (pun intended).
Why this matters beyond the classroom
Understanding compound interest helps students make sense of real financial decisions. A credit card at 20% compounding monthly is far more expensive than it sounds. A savings account at 5% compounding monthly is slightly better than one at 5% compounding annually. These are decisions they will face as adults, and the maths is exactly what they learn in school.
If your child is studying financial mathematics in Years 10 or 11, imSteyn covers compound interest with guided practice that helps students work through problems themselves. Understanding the formula is one thing; knowing when and how to apply it confidently is what gets the marks in assessments.
Written by
the imSteyn Team
We're building an AI maths tutor that helps Australian students discover answers, never just gives them away. Built by parents, for parents.
Try imSteyn Free