Formula guide
Compound Interest Formula
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.
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.
FAQ