How compounding frequency changes the answer
Interest compounded more often earns interest on interest sooner, so 5% compounded monthly is worth more than 5% compounded annually. The effective annual rate is what makes the two comparable.
What this calculator does
- Compounds a lump sum forward at a nominal rate and a chosen compounding frequency.
- Reports the interest earned separately from the final value.
- Converts the nominal rate into an effective annual rate for comparison.
How the calculation works
A nominal rate on its own is not enough to know what you will earn, because it says nothing about how often interest is added. Compounding divides the nominal rate by the number of periods in a year and applies it that many times, so each period's interest starts earning interest immediately rather than waiting until the year end. That is why 5% compounded monthly beats 5% compounded annually, and why daily beats monthly by a smaller further margin — the benefit rises with frequency but with diminishing returns, approaching a ceiling as compounding becomes continuous. The effective annual rate expresses the whole arrangement as the single annual rate that would produce the same result if compounded just once, which is the only sound basis for comparing two products quoted differently. It is the same idea as the AER on a savings account.
The rule
Future value = P × (1 + r ÷ m)^(m × t), where P is the principal, r the nominal annual rate, m the compounding periods per year and t the years. Effective annual rate = (1 + r ÷ m)^m − 1.
Step by step
- Divide the nominal annual rate by the number of compounding periods per year.
- Raise one plus that periodic rate to the power of the total number of periods.
- Multiply by the principal to give the future value.
- Subtract the principal to give the interest earned.
- Compute the effective annual rate to make the quote comparable.
Worked example
£10,000 invested for ten years at a nominal 5% a year, compounded monthly.
What was entered
| Principal amount | £10,000 |
|---|---|
| Nominal annual interest rate | 5% |
| Compounding periods per year | 12 |
| Investment term | 10 years |
The arithmetic
- The monthly rate is 5% ÷ 12, applied 120 times over ten years.
- £10,000 grows to £16,470.09.
- Interest earned is £6,470.09.
- The effective annual rate is 5.1162%, not 5% — the extra 0.1162 points is the value of compounding twelve times rather than once.
- At annual compounding the same £10,000 would reach £16,288.95, so monthly compounding is worth about £181 more over the decade.
What the calculator returns
| Future value | £16,470.09 |
|---|---|
| Interest earned | £6,470.09 |
Key assumptions
- The rate stays fixed for the whole term.
- No money is added or withdrawn during the term.
- Interest is reinvested rather than paid away.
Limitations
- Tax is not modelled. Interest outside an ISA may be taxable beyond the Personal Savings Allowance.
- Inflation is not applied, so the future value is in nominal pounds.
- Real savings and investment rates rarely stay fixed for a decade.
- If interest is paid out rather than reinvested, compounding does not happen at all and the result is simple interest.
Common questions
Why is the effective rate higher than the rate quoted?
Is daily compounding much better than monthly?
Which rate should I compare between accounts?
Related calculators
- Investment Growth Calculator — Add regular contributions to the same compounding engine.
- Stocks & Shares ISA Growth Calculator — Compound the same money inside a tax-free wrapper.
- Pension Growth Calculator — See compounding applied over a full working life.
Official sources
Every figure in this guide was checked against the sources below. Where a source could not confirm a figure, it is marked as requiring verification rather than presented as settled.
- Tax on savings interest — GOV.UKPersonal Savings Allowance on interest earned outside an ISA
- Savings accounts explained — MoneyHelperAER and comparing accounts quoted on different compounding bases