Compound interest is interest earned on both your original money and on the interest already added. Over time this makes balances grow faster than they would with simple interest. For example, £10,000 at 5% a year grows to £16,288.95 after 10 years, rather than the £15,000 that simple interest would give.
Simple versus compound interest
With simple interest you earn interest only on the amount you first put in. £10,000 at 5% earns £500 every year, so after 10 years you have £15,000.
With compound interest each year’s interest is added to the balance, and next year’s interest is calculated on the larger total. After year one you have £10,500, and year two’s interest is £525, not £500. The extra is small at first and grows every year, which is why compounding rewards patience.
The compound interest formula
The standard formula is:
A = P × (1 + r/n)^(n×t)
- A is the final amount.
- P is the starting amount.
- r is the annual interest rate as a decimal (5% is 0.05).
- n is how many times a year interest is added.
- t is the number of years.
For £10,000 at 5% for 10 years, compounded yearly, A = 10,000 × 1.05^10 = £16,288.95.
How compounding frequency matters
The more often interest is added, the more you earn, though the difference is modest. The same £10,000 at 5% for 10 years gives:
| Compounded | Balance after 10 years | Effective yearly rate |
|---|---|---|
| Yearly | £16,288.95 | 5% |
| Monthly | £16,470.09 | 5.12% |
The effective yearly rate is the real annual growth once compounding is included. Savings products often quote an AER, which already shows this effect so that rates can be compared fairly.
Adding regular monthly savings
Most people do not invest one lump sum; they add money each month. Take £5,000 to start, £200 added each month and a 6% rate for 10 years, compounded monthly. The calculator shows:
- Total paid in: £29,000
- Interest earned: £12,872.85
- Final balance: £41,872.85
Roughly 31% of the final balance is interest. Over longer periods the share rises, because earlier deposits have more time to compound. If you have a target in mind, How long to reach a savings goal turns this the other way round and shows how long it takes or how much to save.
The Rule of 72
For a quick mental estimate of how long money takes to double, divide 72 by the annual interest rate. At 6% it is roughly 72 ÷ 6 = 12 years. It is only a rough guide and works best for rates between about 4% and 12%.
Compounding works against borrowers too
The same maths applies to debt. Interest on unpaid credit card balances can compound, and on a mortgage interest is charged on what you still owe, which is why overpaying early helps. See How mortgage repayments are calculated and Loans, APR and car finance: comparing the real cost for how this shows up in loans.
Tax on interest, fees and inflation are not included in these examples, and returns on investments are not guaranteed.
Making compounding work for you
You cannot control the rate, but you can control the other inputs:
- Start early. Time is the biggest driver, because each deposit gets longer to grow.
- Add regularly. Small monthly amounts build up and benefit from compounding.
- Leave interest in. Withdrawing it stops it earning further interest.
- Watch the charges. Fees reduce the return that compounds.
Try changing only one input at a time in the calculator, such as the term from 10 to 20 years, to see how strongly time affects the result. The effect is usually bigger than people expect, which is why the idea is so often described as powerful.
Note: This is general information, not financial advice. The calculators give estimates and assume a fixed rate; real rates and tax treatment vary.
Try the calculator
Enter a starting sum, monthly saving, rate and term in the Compound interest to see how your balance could grow. To work towards a target amount instead, use the Savings goal and interest.
Open the free Compound interest
Frequently asked questions
What is the formula for compound interest?
A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate, n the number of times interest is added each year and t the number of years.
Is monthly compounding much better than yearly?
It is a bit better. At 5% over 10 years, £10,000 grows to £16,470.09 with monthly compounding against £16,288.95 with yearly compounding.
What is the Rule of 72?
A quick estimate of doubling time: divide 72 by the annual interest rate. At 6%, money roughly doubles in 12 years.
Does compound interest apply to debt?
Yes. Interest can be added to what you owe, so balances that are not paid down can grow quickly. Check how your lender or card provider charges interest.