Compound Interest Calculator
See how your money grows over time with compound interest. Supports annual, quarterly, monthly and daily compounding. Includes a growth chart.
What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the interest that has already been earned. In contrast to simple interest — which is calculated only on the original amount — compound interest causes money to grow exponentially over time. Albert Einstein reportedly called compound interest the "eighth wonder of the world," and while the attribution is likely apocryphal, the mathematical power of compounding is very real.
The more frequently interest compounds, the faster a sum grows. Annual compounding adds interest once per year; monthly compounding does so twelve times; daily compounding 365 times. Each compounding period earns interest not just on the original principal but on all previously accumulated interest.
The Compound Interest Formula
| Variable | Meaning |
|---|---|
| A | Final amount (principal + interest) |
| P | Principal (initial investment) |
| r | Annual interest rate (as a decimal — e.g. 5% = 0.05) |
| n | Number of times interest compounds per year |
| t | Time in years |
Formula: A = P × (1 + r/n)^(n×t)
For example: £10,000 at 6% annual interest, compounded monthly, for 20 years: A = 10,000 × (1 + 0.06/12)^(12×20) = £33,102. More than triple the original investment.
Compound vs Simple Interest — Real-World Difference
| Scenario | Simple Interest | Compound (monthly) | Difference |
|---|---|---|---|
| £5,000 at 5% for 10 years | £7,500 | £8,235 | +£735 |
| £10,000 at 7% for 20 years | £24,000 | £40,388 | +£16,388 |
| £1,000 at 10% for 30 years | £4,000 | £19,837 | +£15,837 |
How Compounding Frequency Affects Growth
The more frequently interest compounds, the more you earn — but the differences between monthly and daily compounding are surprisingly small. The biggest jump is between annual and monthly:
| Compounding | £10,000 at 6% for 20 years |
|---|---|
| Annually | £32,071 |
| Quarterly | £32,877 |
| Monthly | £33,102 |
| Daily | £33,199 |
The Rule of 72
The Rule of 72 is a quick mental shortcut for estimating how long it takes money to double at a given interest rate. Simply divide 72 by the annual interest rate: Years to double = 72 ÷ interest rate (%). At 6% interest, your money doubles in approximately 72 ÷ 6 = 12 years. At 9%, it doubles in 8 years. At 3%, it takes 24 years.
Investing £5,000 at age 25 at 7% annual return grows to ~£74,900 by age 65 (40 years). Waiting until 35 to invest the same amount leaves you with ~£38,060 — roughly half. The ten extra years of compounding nearly doubles the final result. Time in the market is the most powerful variable in compound interest.
Frequently Asked Questions
How does compound interest differ from simple interest?
Simple interest is calculated only on the original principal. If you invest £1,000 at 5% simple interest for 10 years, you earn £50 per year — always on the original £1,000 — for a total of £1,500. With compound interest, each year's interest is added to the principal, so the next year you earn interest on a larger amount. The same £1,000 at 5% compounded annually for 10 years grows to £1,629 — an extra £129 over simple interest, and the gap widens dramatically over longer periods.
What does APR vs APY mean, and which should I use?
APR (Annual Percentage Rate) is the nominal annual rate without considering compounding. APY (Annual Percentage Yield) — also called EAR (Effective Annual Rate) — accounts for compounding and represents the actual return you earn in a year. A savings account advertising 6% APR with monthly compounding has an APY of 6.17%. For comparing savings accounts and investments, APY is the more meaningful number. For loans, lenders are typically required to disclose APR.
How long does it take to double my money?
Use the Rule of 72: divide 72 by the annual interest rate to get the approximate number of years to double. At 6% it takes ~12 years; at 8% ~9 years; at 12% ~6 years. This rule works well for rates between 1% and 20%. For higher rates, use the Rule of 69.3 (or just use this calculator for precise results).
Does compound interest work against you on debt?
Yes — and this is exactly why high-interest debt (credit cards, payday loans) is so dangerous. A £3,000 credit card balance at 20% APR, paid off only with minimum payments, can take over 10 years to clear and cost more than £3,000 in interest — more than the original debt. The same mathematical force that builds wealth in savings accounts works against you when you carry a balance at a high rate.
Is compound interest taxed?
In most countries, interest income is taxable in the year it's received or credited, even if you don't withdraw it. In the UK, ISAs (Individual Savings Accounts) shelter interest from tax. In the US, 401(k) and IRA accounts offer tax deferral or tax-free growth. Investing inside tax-advantaged accounts significantly improves the real compound growth you keep after tax.
What is continuous compounding?
Continuous compounding is the mathematical limit of increasing compounding frequency — imagine compounding every millisecond, every microsecond, indefinitely. The formula is A = P × e^(r×t), where e is Euler's number (~2.71828). In practice, the difference between daily and continuous compounding is negligible (a fraction of a percent). Continuous compounding is mainly used in financial mathematics and derivatives pricing rather than everyday banking products.