What is compound interest?
Compound interest means earning interest on your interest. Each time interest is added to your account, the next interest payment is calculated on the larger balance, so your money grows faster and faster over time. Simple interest, by contrast, is only ever paid on the original amount.
The effect is small over a year or two but becomes dramatic over decades. That is why starting to save early, and leaving interest in the account rather than withdrawing it, makes such a difference.
The compound interest formula
For a single lump sum, the balance after t years is:
A = P × (1 + r/n) ^ (n × t)
where P is the starting amount, r is the annual rate as a decimal, n is the number of times interest is compounded per year (12 for monthly, 365 for daily) and t is the number of years.
With regular deposits, each deposit grows for a shorter time. The calculator handles this by working month by month: it converts your chosen compounding frequency into an equivalent monthly growth factor, (1 + r/n) ^ (n/12), adds that month's interest, then adds your monthly deposit at the end of the month.
AER and compounding frequency
UK savings accounts quote an AER (Annual Equivalent Rate), which shows what the interest would be over a year once compounding is taken into account. The calculator shows this as the equivalent annual rate: AER = (1 + r/n) ^ n − 1.
The more often interest is compounded, the higher the AER for the same nominal rate, although the difference is modest. For £10,000 at a nominal 5% for one year:
- If your bank quotes an AER and pays interest annually, enter the AER and choose yearly.
- If you only know the AER but interest is paid monthly, entering the AER with monthly compounding will slightly overstate growth.
| Compounding | Interest after 1 year | AER |
|---|---|---|
| Yearly | £500.00 | 5.00% |
| Quarterly | £509.45 | 5.09% |
| Monthly | £511.62 | 5.12% |
| Daily | £512.67 | 5.13% |
Tax on savings interest: Personal Savings Allowance and ISAs
In the UK, interest is paid gross (without tax deducted). Most people pay no tax on it because of the Personal Savings Allowance (PSA). Interest above your allowance is taxed at your Income Tax rate, usually collected through your tax code or Self Assessment.
Interest earned inside an ISA is completely tax-free and does not use up your PSA. You can pay in up to £20,000 per tax year across all your ISAs. Lower earners may also benefit from the starting rate for savings, which can make up to £5,000 of interest tax-free if your other income is low.
- The tax field in this calculator applies one flat rate to all interest. Because the PSA makes the first part tax-free, enter your effective rate: tax rate × (interest − allowance) ÷ interest.
- Leave tax at 0% for ISA savings or if your yearly interest stays within your allowance.
- The calculator deducts tax as each month's interest is added, so only after-tax interest compounds. In reality HMRC collects the tax later, so the result is a close, slightly cautious estimate.
| Your Income Tax band | Personal Savings Allowance | Tax on interest above it |
|---|---|---|
| Basic rate (20%) | £1,000 | 20% |
| Higher rate (40%) | £500 | 40% |
| Additional rate (45%) | £0 | 45% |
Worked example 1: a £10,000 lump sum for 5 years
£10,000 at 4.5% a year, compounded monthly, 5 years, no deposits, no tax
AER = (1 + 0.045/12) ^ 12 − 1 = 4.59%
Balance after 1 year = £10,459.40; after 2 years = £10,939.90
Balance after 5 years = £10,000 × (1.00375) ^ 60 = £12,517.96
Interest earned = £2,517.96, compared with £2,250 under simple interest
Worked example 2: saving £200 a month
£5,000 start, £200 a month, 4% compounded monthly, 10 years
Total paid in = £5,000 + £200 × 120 = £29,000
Balance after 1 year = £7,648.20
Balance after 10 years = £36,904.12
Interest earned = £7,904.12, about 27% on top of what you paid in
Worked example 3: tax for a higher-rate taxpayer
£50,000 at 4.5% compounded monthly for 1 year, higher-rate taxpayer
Interest before tax (tax 0%) = £2,296.99
Higher-rate PSA = £500, so taxable interest = £2,296.99 − £500 = £1,796.99
Tax = £1,796.99 × 40% = £718.80
Effective tax rate = £718.80 ÷ £2,296.99 = about 31.3%
Entering 31.3% in the tax field gives interest after tax of £1,567.84 and a balance of £51,567.84
In a Cash ISA the same savings would keep the full £2,296.99.
Worked example 4: £250 a month for 20 years
£0 start, £250 a month, 5% compounded monthly, 20 years
Total paid in = £250 × 240 = £60,000
Balance after 10 years = £38,820.57
Balance after 20 years = £102,758.42
Interest earned = £42,758.42; in the 20th year alone interest adds £4,921.74, more than in the first five years combined
Common mistakes and tips
- Mixing up AER and nominal rate. Enter the nominal rate with the matching compounding frequency, or the AER with yearly compounding.
- Ignoring inflation. Your balance in pounds grows, but if inflation is higher than your after-tax rate, its buying power falls.
- Assuming rates stay fixed. Easy-access and variable rates change; fixed-rate bonds lock your money away for the term. Treat long projections as illustrations.
- Forgetting the PSA is shared. All your interest from all accounts counts towards one allowance, which higher savings rates can quickly use up.
- Not using your ISA allowance. Moving savings into an ISA is often the simplest way to keep interest tax-free.
- For investments such as stocks and shares, returns are not guaranteed and can fall as well as rise; the calculator assumes a steady rate.