What is Compound Interest?
Last updated: 1 May 2025
Compound interest is interest calculated on both your original principal and all the interest that has already accumulated. In contrast to simple interest — which only applies to the original amount — compound interest creates exponential growth over time.
The famous (possibly apocryphal) quote attributed to Albert Einstein: "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it." Whether Einstein actually said this is debated — but the mathematics are not.
The compound interest formula
The standard formula for compound interest is:
Where:
- A = Final amount (what your investment grows to)
- P = Principal (the initial investment amount)
- r = Annual interest rate expressed as a decimal (e.g. 8% = 0.08)
- n = Number of times interest compounds per year (12 for monthly, 365 for daily)
- t = Time in years
A worked example
You invest $10,000 at 8% per year, compounded monthly, for 10 years.
- P = 10,000
- r = 0.08
- n = 12
- t = 10
A = 10,000 × (1 + 0.08/12)^(12×10) = 10,000 × (1.006667)^120 = $22,196
Of the $22,196 final balance, $10,000 is your original investment. The remaining $12,196 is pure compound interest — money you earned without any additional effort.
Compare this to simple interest: 8% per year on $10,000 for 10 years = $10,000 × 0.08 × 10 = $8,000 in interest, giving a total of $18,000. Compound interest produces $4,196 more over the same period.
See this in action with our compound interest calculator, or view a specific scenario like $10,000 at 8% for 10 years.
How compounding frequency affects growth
The more frequently interest compounds, the more you earn. For $10,000 at 8% for 10 years:
| Compounding frequency | Final balance | Interest earned |
|---|---|---|
| Annually (n=1) | $21,589 | $11,589 |
| Quarterly (n=4) | $22,080 | $12,080 |
| Monthly (n=12) | $22,196 | $12,196 |
| Daily (n=365) | $22,253 | $12,253 |
The difference between annual and daily compounding is only $664 here — compounding frequency matters less than the interest rate and time horizon.
The effect of time: why starting early matters
Time is the most powerful variable in compound interest. Consider two investors:
- Investor A starts at age 25, invests $500/month until age 35 (10 years, then stops). Total invested: $60,000.
- Investor B starts at age 35, invests $500/month until age 65 (30 years). Total invested: $180,000.
At 7% annual return, at age 65: Investor A has approximately $602,000. Investor B has approximately $567,000. Investor A invested less money but ends up with more — purely because of the extra 10 years of compounding.
Model this yourself: $500/month at 7% for 10 years vs $500/month at 7% for 30 years.
Compound interest on debt: the other side
The same mathematics that builds wealth also works against you on debt. Credit card debt at 20% compounded monthly that you only pay the minimum on will grow rapidly. A $5,000 credit card balance at 20% with minimum payments of 2% of balance takes over 30 years to pay off and costs over $13,000 in interest.
This is why the same understanding that makes investors wealthy also drives financial advisers to recommend paying off high-interest debt before investing.
The effective annual rate (EAR)
When interest compounds more frequently than annually, the actual annual return is higher than the stated nominal rate. The effective annual rate formula is:
At 8% nominal with monthly compounding: EAR = (1 + 0.08/12)^12 − 1 = 8.30%. This is the true annual return, and what our compound interest calculator displays.
The Rule of 72
A quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
- At 6%: doubles in 72 ÷ 6 = 12 years
- At 8%: doubles in 72 ÷ 8 = 9 years
- At 10%: doubles in 72 ÷ 10 = 7.2 years
Read more in our Rule of 72 guide.
Key takeaways
- Compound interest earns interest on interest — creating exponential, not linear, growth
- The formula is A = P(1 + r/n)^(nt)
- Time is the most powerful variable — starting early matters enormously
- Compounding frequency has a smaller effect than rate or time
- Compound interest works against you on debt just as powerfully as it works for you on savings
Related guides: Rule of 72 · Superannuation guide · What is TDEE?