Compound Interest Explained — How Your Money Grows Over Time
What compound interest is, how it is calculated, why it is so powerful for savings and investments, and how to use it against debt.
Albert Einstein is often (probably apocryphally) credited with calling compound interest the eighth wonder of the world. Whether or not he said it, the sentiment is right: the ability of money to grow exponentially over time is one of the most powerful forces in personal finance.
See it in action with our Compound Interest Calculator.
What Is Compound Interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus the interest that has already accumulated.
The difference becomes dramatic over long periods.
Example — £10,000 at 5% over 30 years:
| Simple interest | Compound interest (annual) | |
|---|---|---|
| After 10 years | £15,000 | £16,289 |
| After 20 years | £20,000 | £26,533 |
| After 30 years | £25,000 | £43,219 |
The same starting sum, the same interest rate, but a difference of over £18,000 at the 30-year mark.
The Formula
A = P × (1 + r/n)^(n × t)Where:
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (as a decimal, e.g. 0.05 for 5%)
- n = number of times interest is compounded per year
- t = time in years
Interest earned = A − P
Compounding Frequency Matters
Interest can compound annually, monthly, weekly, or even daily. More frequent compounding means slightly faster growth.
£10,000 at 5% over 10 years:
| Compounding | Final value |
|---|---|
| Annually | £16,289 |
| Quarterly | £16,436 |
| Monthly | £16,471 |
| Daily | £16,487 |
The difference between annual and daily compounding is modest at moderate rates, but becomes more significant at higher rates or over longer periods.
The Rule of 72
A quick mental shortcut: divide 72 by the interest rate to estimate how many years it takes your money to double.
| Interest rate | Years to double |
|---|---|
| 3% | 24 years |
| 5% | 14.4 years |
| 7% | 10.3 years |
| 10% | 7.2 years |
This works because of the mathematics of exponential growth — it is a rough approximation but accurate enough for planning purposes.
Why Starting Early Makes Such a Difference
The most powerful input in compound interest is time. An extra decade at the start is worth far more than additional contributions later.
Example — two investors, same total contributions:
| Investor A | Investor B | |
|---|---|---|
| Invests | £5,000/year for 10 years then stops | £5,000/year for 30 years |
| Period | Age 25–35 | Age 35–65 |
| Total invested | £50,000 | £150,000 |
| Final value at 7% | £602,070 | £472,304 |
Investor A — who stopped contributing 30 years earlier — ends up with more money, because their investments had 30 extra years to compound. This is why financial advisers consistently emphasise starting early.
Compound Interest in Reverse: The Cost of Debt
Compound interest works just as powerfully against you when it comes to debt, particularly credit cards.
A £5,000 credit card balance at 25% APR, with minimum payments of 2% of the balance:
- You would pay the debt off in approximately 35 years
- You would pay over £14,000 in interest — nearly three times the original balance
Use our Credit Card Payoff Calculator to see how long it will take to pay off your balance, and our Loan Calculator for fixed-term borrowing.
ISAs and Tax-Free Compounding
In the UK, compounding in a Stocks and Shares ISA is particularly powerful because gains and income are free from capital gains tax and income tax. The full ISA allowance for 2025/26 is £20,000 per person per year.
Over decades, the tax saving on compound returns can itself become a substantial sum.