Money & everyday · 3 min read
Compound Interest Formula Explained With Worked Examples
The formula
A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the compoundings per year and t the years.
Annual compounding: 1000 at 5% for 10 years
Order-of-operations steps 3 steps
Start: 1000 × (1 + 0.05)^10
- Add
1 + 0.05 = 1.05→ 1000 × 1.05^10 - Exponent
1.05^10 = 1.628894627→ 1000 × 1.628894627 - Multiply
1000 × 1.628894627 = 1628.894627→ 1628.894627
How compounding frequency changes the result
| Compounding | Value after 10 years |
|---|---|
| Simple interest | 1,500.00 |
| Annually (n = 1) | 1,628.89 |
| Quarterly (n = 4) | 1,643.62 |
| Monthly (n = 12) | 1,647.01 |
| Daily (n = 365) | 1,648.66 |
| Continuous (Pe^(rt)) | 1,648.72 |
More frequent compounding helps, but the gain levels off — the continuous case uses Euler’s number e.
Growth over time
| Years | Balance (annual, 5%) |
|---|---|
| 1 | 1,050.00 |
| 5 | 1,276.28 |
| 10 | 1,628.89 |
| 20 | 2,653.30 |
| 30 | 4,321.94 |
Time matters more than the exact rate: the curve bends upward. Compare the same idea with simple interest.
Checking your work
Use the scientific calculator and the exponent calculator. This is a maths explanation, not financial advice.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal; compound interest is calculated on the principal plus accumulated interest.
How do I find the rate?
Rearrange: r = n((A/P)^(1/(nt)) − 1).
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