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
Worked example 2: what time does to regular saving
Time is the biggest lever, and the compound interest calculator’s engine shows it clearly. Suppose you save £300 a month from nothing at 5% a year, compounded monthly:
| Term | You pay in | Interest earned | Final balance |
|---|---|---|---|
| 20 years | £72,000 | £51,310.10 | £123,310.10 |
| 30 years | £108,000 | £141,677.59 | £249,677.59 |
Ten extra years adds only £36,000 of your own money, but the balance more than doubles, because interest in the later years is earned on a much bigger pot. By year 30, interest is more than half the balance.
Now compare saving more for less time. £600 a month at 5% for 10 years pays in £72,000, the same as £300 for 20 years, yet it ends at £93,169.37 against £123,310.10. Starting earlier with a smaller amount beat saving twice as much later, with the same total paid in. These are illustrations with a fixed rate; real returns vary and savings rates change.
Step-by-step: working out growth by hand
For a lump sum with no further deposits:
- Convert the rate to a decimal: 4% is 0.04.
- Divide by the number of periods a year, n. For monthly, 0.04 ÷ 12 = 0.003333.
- Add 1: 1.003333.
- Raise it to the power n × t. For 10 years monthly, that is 120.
- Multiply by the starting amount.
£10,000 at 4% for 10 years, compounded monthly, ends at £14,908.33. The same sum at 6% reaches £18,193.97. Two percentage points more rate lifts the ten-year growth from £4,908 to £8,194, which is about two-thirds more. Most pocket calculators and spreadsheets have a power key or the POWER function to do step 4.
Real returns: allowing for inflation
A balance that grows is not the same as buying power that grows. If your savings earn 5% and prices rise 3%, your real growth is roughly 1.94%, found by dividing 1.05 by 1.03 and subtracting 1. After 10 years, £10,000 at 5% reaches £16,288.95, but in today’s money it is worth about £12,120. When rates are below inflation, the real value falls even as the number gets bigger. The guide to UK inflation explained shows how to adjust figures this way.
Rule of 72 in practice
The rule is a quick check rather than an exact answer. Exact doubling times, from the logarithm formula, are about 23.4 years at 3%, 11.9 years at 6% and 8.0 years at 9%. The rule gives 24, 12 and 8, so it lands close. It works in reverse too: if you want to double in 9 years, you need roughly 8% a year.
Common mistakes
- Mixing up nominal and effective rates. A 5% rate compounded monthly is an effective 5.12% a year.
- Forgetting tax and fees. Interest outside an ISA may be taxable, and charges reduce what compounds.
- Assuming steady returns. Investments rise and fall; a fixed average is a planning tool, not a promise.
- Ignoring debt. Interest on a credit card can compound against you faster than savings earn. See Credit card interest explained: APR, minimums and payoff time.
Glossary
- Principal: the starting amount.
- AER: annual equivalent rate, the yearly rate once compounding is included.
- Nominal rate: the quoted rate before compounding is allowed for.
- Real return: growth after taking inflation away.
- Term: how long the money is left to grow.
Compound interest and your mortgage or loan
Compounding is not only for savers. On a repayment mortgage, interest is worked out on the balance still owed, so early payments are mostly interest and later ones mostly capital. Paying a little extra early cuts the balance that interest is charged on, which is why overpayments have more effect in the first years. Check with your lender for any overpayment limits or early repayment charges before you do this. The same logic applies to a personal loan or car finance, where the APR tells you the yearly cost including compounding. Both are covered in How mortgage repayments are calculated and Loans, APR and car finance: comparing the real cost.
Putting it to use: a simple checklist
- Decide what the money is for and when you need it. Short-term cash belongs in an easy-access account; money you will not need for many years can take more risk, with the possibility of loss.
- Work out a monthly amount you can keep up. A smaller amount you never miss beats a bigger one you stop after a year.
- Use the ISA allowance and any employer pension contributions, since tax-free growth and free money compound just like interest. Check GOV.UK for the current ISA limit.
- Set the payment up by standing order so it happens automatically.
- Review once a year: check the rate, the charges and whether you can pay in more.
- Resist the urge to dip in. Every withdrawal removes the growth that money would have earned for the rest of the term.
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.
Does it matter when interest is paid, monthly or yearly?
Slightly. More frequent payment means interest starts earning interest sooner, but the gap is small compared with the effect of the rate and the term.
How can I compare two savings accounts?
Compare the AER, which already includes compounding, and check access rules, bonus rates that expire and any limits on deposits.
Is the calculator's monthly saving added at the start or end of the month?
The calculator adds each monthly saving at the end of the month. Adding at the start would give a slightly higher balance.
Can I use it for investments?
You can, with an assumed average growth rate, but investment returns are not guaranteed and vary year to year, so treat the result as an illustration.