Overview
Compound interest is useful, but it is often presented as if a small deposit inevitably becomes a fortune. The arithmetic is less dramatic and more practical.
Your result depends on the starting balance, contributions, rate, time and whether interest stays in the account. A projection is only as reliable as those assumptions.
Quick Answer
Compound interest means earning interest on interest already added to your savings. If you leave the return in the account, the next calculation can apply to a larger balance.
It does not guarantee a constant rate, protect purchasing power or turn a risky investment into a savings account. Use it as a calculation method, not a promise.
A Three-Year Example
Assume £5,000 earns a fixed 4% each year, interest is added annually and nothing is withdrawn. Ignore tax and fees.
| Year | Opening balance | Interest | Closing balance |
|---|---|---|---|
| 1 | £5,000.00 | £200.00 | £5,200.00 |
| 2 | £5,200.00 | £208.00 | £5,408.00 |
| 3 | £5,408.00 | £216.32 | £5,624.32 |
In the second year, £8 of the interest is earned on the previous year's £200. In the third, interest is calculated on both the original savings and all retained interest.
If you withdrew each year's £200 instead, the account would stay at £5,000 and the three years' interest would total £600. With the stated compounding assumptions it totals £624.32.
The Formula and Its Limits
For an annual effective rate with no extra payments, the calculation is:
Future balance = starting balance × (1 + annual rate) raised to the number of years.
In the example, £5,000 × 1.04 × 1.04 × 1.04 gives £5,624.32.
The formula assumes the rate applies for the whole period and the interest remains available to earn more interest. If the rate changes, calculate each period at its own rate rather than extending today's rate indefinitely.
A fixed account might guarantee a rate for one or two years, not the next decade.
AER Already Reflects Compounding Assumptions
AER is intended to help compare annual returns. Do not take an AER, divide it by 12 and then compound that result monthly as though it were a nominal annual rate; that can overstate the return.
If you need an equivalent monthly rate from a 4% effective annual rate, it is the twelfth root of 1.04 minus 1, about 0.3274%.
Actual account interest may be calculated daily and credited monthly or annually. Read the product terms and use our AER versus gross-rate guide when comparing quoted rates.
Monthly Saving Is Not a Lump Sum Invested All Year
If you save £200 each month, the final year's total contributions are £2,400. But the last £200 has not earned interest for the same length of time as the first.
Applying the annual rate to the full £2,400 as though it was deposited on day one exaggerates the first-year interest.
A useful calculator needs to know whether contributions happen at the beginning or end of each month. It should also distinguish money you added from interest earned.
Our regular-saver guide explains why an attractive regular-saver rate can still produce a modest first-year cash return.
Tax and Withdrawals Change What Compounds
If interest is taxable, the after-tax benefit may be smaller than the gross projection. If you withdraw the interest to pay bills, it cannot also remain in the account earning more interest.
Inside a valid ISA, the tax treatment is different, but the subscription rules still apply. Read ISA interest and allowances rather than assuming an account balance is the same thing as new contributions.
Fees can also reduce the amount left to grow. Include them where relevant instead of showing only the headline return.
Inflation Is a Separate Calculation
A rising balance does not necessarily buy more. If prices increase faster than the account's after-tax return, purchasing power can fall.
That does not make accessible cash useless. An emergency fund serves a different purpose from money invested for a distant goal.
Avoid moving money needed soon into volatile investments just because a compounding chart uses a higher assumed return. An average investment return is not a guaranteed interest rate.
Use Projections to Plan Contributions
Calculate several scenarios rather than one precise-looking future balance. Vary the rate and the contribution, then ask which changes you can actually control.
For a near-term goal, your monthly saving amount may matter more than a small rate difference. A plan that requires an implausible return needs a longer timescale, more contributions or a smaller target.
Our short-term savings guide helps match access to the goal.
Frequently Asked Questions
Explore savings guides. All rates here are hypothetical and the examples exclude tax unless stated.
