How to Calculate Compound Interest on Savings
The compound interest formula explained step by step, with worked examples for annual, monthly and daily compounding, regular deposits, and AER.
Published by Calculator.uk.com · Updated 21 October 2026 · Our methodology
Quick answer
Compound interest on savings is calculated with A = P × (1 + r/n)n×t. P is your starting balance, r is the annual rate as a decimal, n is how many times a year interest is added and t is the number of years. For example, £10,000 at 4% compounded monthly for 3 years grows to £11,272.72. Use the free calculator below to run your own numbers, with regular deposits and a growth chart included.
Compound interest savings calculator
Enter your figures and press Calculate. Results show in dollars, but the maths is the same in any currency, so £, € or $ amounts all work.
Enter values to calculate compound interest
What compound interest means
With simple interest you earn interest only on the money you originally deposited. With compound interest, each interest payment is added to your balance, and the next payment is calculated on that larger balance. Your interest starts earning interest, so savings grow faster every year you leave them alone.
Over 3 years at 4%, £10,000 earns £1,200 with simple interest, or £1,248.64 with annual compounding. That gap looks small, but it widens every year. After 30 years the simple-interest balance is £22,000, while the annually compounded balance is £32,433.98.
The compound interest formula, step by step
- A is the final balance
- P is the principal, the amount you start with
- r is the annual interest rate as a decimal (4% = 0.04)
- n is the number of compounding periods per year (1 annual, 4 quarterly, 12 monthly, 365 daily)
- t is the time in years
Steps
- Convert the rate to a decimal: divide the percentage by 100.
- Divide the rate by n to get the rate per period.
- Add 1 to the result.
- Raise that to the power of n × t, the total number of periods.
- Multiply by P. Subtract P from the result to get the interest earned.
Worked example 1: annual compounding, year by year
£10,000 in a savings account paying 4% a year, compounded annually, left for 3 years:
| Year | Start balance | Interest (4%) | End balance |
|---|---|---|---|
| 1 | £10,000.00 | £400.00 | £10,400.00 |
| 2 | £10,400.00 | £416.00 | £10,816.00 |
| 3 | £10,816.00 | £432.64 | £11,248.64 |
With the formula: A = 10,000 × (1 + 0.04/1)1×3 = 10,000 × 1.124864 = £11,248.64. The second year's interest (£416) is higher than the first (£400) because it is earned on the first year's interest as well.
Worked example 2: how compounding frequency changes the result
The same £10,000 at 4% for 3 years, with interest added more often:
| Compounding | Calculation | Balance after 3 years |
|---|---|---|
| Annually (n = 1) | 10,000 × 1.043 | £11,248.64 |
| Quarterly (n = 4) | 10,000 × 1.0112 | £11,268.25 |
| Monthly (n = 12) | 10,000 × (1 + 0.04/12)36 | £11,272.72 |
| Daily (n = 365) | 10,000 × (1 + 0.04/365)1095 | £11,274.89 |
More frequent compounding helps, but the difference between monthly and daily is only a couple of pounds. The interest rate and the time you leave the money invested matter far more than the compounding frequency.
Worked example 3: saving a fixed amount every month
Most people add to their savings regularly. For a fixed deposit PMT at the end of every month, with monthly compounding, the deposits grow to:
Start with £10,000, add £200 a month, earn 4% compounded monthly, and leave it for 10 years:
- Starting balance: 10,000 × (1 + 0.04/12)120 = £14,908.33
- Monthly deposits: 200 × ((1 + 0.04/12)120 − 1) ÷ (0.04/12) = £29,449.96
- Final balance: £44,358.29, made up of £34,000 paid in and £10,358.29 interest
| Years | Total paid in | Balance at 4% | Interest earned |
|---|---|---|---|
| 5 | £22,000 | £25,469.76 | £3,469.76 |
| 10 | £34,000 | £44,358.29 | £10,358.29 |
| 20 | £58,000 | £95,580.75 | £37,580.75 |
| 30 | £82,000 | £171,944.86 | £89,944.86 |
Notice how interest overtakes contributions over time. In years 21 to 30 the balance grows by £76,364, of which only £24,000 is new money. To check these figures, enter £10,000, £200 a month, 4%, monthly compounding and the number of years in the calculator above.
AER, gross rate and what to type in
Banks quote savings rates in two ways. The gross (nominal) rate is the yearly rate before compounding. The AER (annual equivalent rate), called APY in the US, shows what you would earn if interest were paid once a year, so it already includes compounding:
A 4% gross rate paid monthly is an AER of 4.07%. Going the other way, an account advertised at 4.5% AER that pays monthly has a gross rate of 4.41%. If you only know the AER, enter it with annual compounding. Entering the AER with monthly compounding would count the compounding twice.
Quick estimate: the Rule of 72
To estimate how long money takes to double, divide 72 by the interest rate. At 4%, 72 ÷ 4 = 18 years. The exact answer, ln(2) ÷ ln(1.04), is 17.7 years. The rule is a good mental check, but use the formula or the calculator for real figures.
Things the formula does not include
- Tax. Interest may be taxable depending on where you live and your allowances. Tax-free wrappers such as an ISA in the UK keep the full compounded amount.
- Rate changes. Variable-rate accounts change over time. Treat the result as a projection at today's rate.
- Inflation. A 4% return with 3% inflation is roughly 1% growth in real purchasing power.
- Fees and withdrawals. Taking money out stops that money compounding. Withdrawals also reset the growth on any interest you take.
Frequently asked questions
How do I work out compound interest on my savings online for free?
Use the free compound interest calculator on this page: enter your starting balance, how much you add each month, the interest rate, how often interest is compounded and the number of years. It applies the standard formula A = P(1 + r/n)^(nt) plus the future value of your monthly deposits and shows the final balance, the total you paid in, the interest earned and a year-by-year growth chart. No sign-up is needed.
What is the formula for compound interest?
A = P × (1 + r/n)^(n × t), where A is the final balance, P is the starting amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year and t is the number of years. The interest earned is A − P. If you also save a fixed amount PMT every month and interest compounds monthly, add PMT × ((1 + r/12)^(12t) − 1) ÷ (r/12).
How much is £10,000 worth after 10 years at 4% compound interest?
Compounded annually, £10,000 at 4% grows to £14,802.44 after 10 years. Compounded monthly it grows to £14,908.33. Adding £200 a month on top, with monthly compounding, gives £44,358.29 after 10 years, of which £34,000 is money paid in and £10,358.29 is interest.
Should I enter the AER or the gross rate?
AER (annual equivalent rate) already includes the effect of compounding within the year. If you only know the AER, enter it with annual compounding and the lump-sum result will be correct. If the account states a gross or nominal rate that is paid monthly, enter that rate with monthly compounding. Entering an AER with monthly compounding would slightly overstate your interest.
What is the source for the compound interest formula used here?
The formula is the standard time-value-of-money result for compound growth, A = P(1 + r/n)^(nt), with the ordinary-annuity formula for regular end-of-period deposits, as set out in corporate finance and actuarial mathematics textbooks. The AER definition follows the UK regulatory convention for savings products, in which AER = (1 + r/n)^n − 1 expresses what the rate would be if interest were paid and compounded once a year.