Formula guide
Compound Interest Formula
By Compound Interest Tools · Updated · Calculation method
Understand A = P(1 + r/n)^(nt), what each part means, and how to calculate annual, monthly or daily compounding.
The compound interest formula
The standard compound interest formula is:
A = P(1 + r/n)^(n × t)This calculates the future value of a starting amount when interest is compounded a fixed number of times per year.
What each part means
- A = final amount after interest has compounded.
- P = principal, or starting amount.
- r = annual interest rate as a decimal. For 5%, use 0.05.
- n = number of compounding periods per year.
- t = time in years.
Compounding frequency values
| Frequency | n | Formula version |
|---|---|---|
| Annual | 1 | A = P(1 + r)^t |
| Quarterly | 4 | A = P(1 + r/4)^(4t) |
| Monthly | 12 | A = P(1 + r/12)^(12t) |
| Daily | 365 | A = P(1 + r/365)^(365t) |
Worked example: £10,000 at 5% for 10 years
For £10,000 at 5% for 10 years compounded monthly, use:
- P = 10000
- r = 0.05
- n = 12
- t = 10
A = 10000(1 + 0.05/12)^(12 × 10)The estimated final balance is £16,470.09, with estimated interest of £6,470.09.
Open this formula example in the calculator.
For more rate and term comparisons, see the compound interest tables. To practise the calculation and check your working, use the worksheets with worked answers.
Formula examples by rate
| Rate | 5 years | 10 years | 20 years |
|---|---|---|---|
| 3% | £11,616.17 | £13,493.54 | £18,207.55 |
| 5% | £12,833.59 | £16,470.09 | £27,126.40 |
| 7% | £14,176.25 | £20,096.61 | £40,387.39 |
| 10% | £16,453.09 | £27,070.41 | £73,280.74 |
Common mistakes
- Entering 5 instead of 0.05 when using the formula manually.
- Forgetting to multiply the number of years by the compounding frequency.
- Using the basic formula for a scenario that includes monthly deposits.
- Assuming a fixed rate when the real product has a variable rate.
What about regular deposits?
The formula above is for a starting amount only. If you add regular deposits, each deposit has its own compounding period. The website calculator handles this by modelling the calculation month by month.
Read more: compound interest with monthly deposits.
Calculate it yourself
Use the free compound interest calculator to adjust the amount, rate, term, compounding frequency and regular deposits.
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