Compound interest is interest earned on both your original money and the interest it has already earned. Each period's interest is added to the balance, so the next period's interest is calculated on a bigger sum. £10,000 at 4% a year, compounded annually, grows to about £14,802 after 10 years, compared with £14,000 under simple interest.
That difference grows the longer you leave the money and the more often interest is added. This guide explains the formula, how compounding frequency works, what AER means compared with the gross rate, how regular saving compounds, and what tax, ISAs and inflation do to the real result in the 2026/27 tax year. It's an explanation of how the maths works, not financial advice.
To test your own figures, use our free compound interest calculator, which handles lump sums, regular deposits and different compounding frequencies.
Key takeaways
- Compound interest means earning interest on past interest, using A = P x (1 + r/n)^(nt).
- £10,000 at 4% for 10 years grows to £14,802.44 compounded yearly and £14,908.33 compounded monthly.
- AER shows what a rate would earn over a year with compounding included, so it's the fair way to compare savings accounts.
- For 2026/27 the ISA allowance is £20,000, and inflation reduces what your savings can buy, so compare your rate with it.
Simple vs compound interest
| Year | Simple interest at 4% on £10,000 | Compound interest at 4% (yearly) |
|---|---|---|
| 1 | £10,400.00 | £10,400.00 |
| 2 | £10,800.00 | £10,816.00 |
| 5 | £12,000.00 | £12,166.53 |
| 10 | £14,000.00 | £14,802.44 |
| 20 | £18,000.00 | £21,911.23 |
| 30 | £22,000.00 | £32,433.98 |
In year one they're identical. By year 30, compounding has earned over £10,000 more, entirely from interest on interest. Time does most of the work.
Compound interest explained: the formula
A = P × (1 + r/n)^(n × t)
- A is the final amount
- P is the starting amount (principal)
- r is the annual interest rate as a decimal (4% = 0.04)
- n is how many times a year interest is added (1 for yearly, 12 for monthly)
- t is the number of years
The interest earned is A − P.
Worked example
£10,000 at 4% compounded monthly for 10 years:
- r/n = 0.04 ÷ 12 = 0.003333
- n × t = 12 × 10 = 120
- (1.003333)^120 ≈ 1.4908
- A = £10,000 × 1.4908 ≈ £14,908.33
How compounding frequency changes the result
Same £10,000, same 4% gross rate, 10 years:
| Interest added | Final balance | Interest earned |
|---|---|---|
| Yearly | £14,802.44 | £4,802.44 |
| Monthly | £14,908.33 | £4,908.33 |
| Daily | £14,917.92 | £4,917.92 |
More frequent compounding helps, but the jump from monthly to daily is small. The rate itself matters far more than the frequency.
AER vs gross rate
Savings accounts show two rates, and the difference is about compounding:
- Gross rate is the contractual rate before tax, not adjusted for how often interest is paid.
- AER (annual equivalent rate) shows what the rate would be if interest were paid and compounded once a year. It builds in the effect of compounding frequency so you can compare accounts fairly.
The conversion is: AER = (1 + gross rate ÷ n)^n − 1
A 4% gross rate paid monthly has an AER of about 4.074%. A 4% gross rate paid yearly has an AER of exactly 4%. So when you compare two accounts, compare the AERs, not the gross rates. AER doesn't include one-off bonuses that end after a set period, so check whether a headline rate drops later.
Regular saving: compounding monthly deposits
Most people don't save one lump sum. For regular deposits made at the end of each period, the future value is:
FV = PMT × ((1 + r/n)^(n × t) − 1) ÷ (r/n)
Saving £200 a month at 4% compounded monthly for 10 years:
- You pay in £24,000.
- The balance reaches about £29,449.96.
- Compounding has added about £5,450.
Starting earlier has a bigger effect than saving a little more later, because early deposits have longer to compound. Compare two savers, both at 4% compounded monthly:
| Saver | Monthly deposit | Years | Total paid in | Final balance |
|---|---|---|---|---|
| Starts early | £200 | 20 | £48,000 | £73,354.93 |
| Starts later, saves double | £400 | 10 | £48,000 | £58,899.92 |
Both pay in exactly the same amount. The early starter ends up about £14,455 better off purely because their money had longer to earn interest on interest. These are illustrations at a fixed rate; real savings rates change over time.
The rule of 72
A quick way to estimate how long money takes to double: divide 72 by the annual rate. At 4%, 72 ÷ 4 = 18 years. The exact answer for yearly compounding at 4% is about 17.7 years, so the shortcut is close enough for a quick sense check. It works the other way too: at 3% inflation, prices roughly double in 24 years.
Tax on savings interest in 2026/27
Interest is taxable income, but most people get some tax-free. GOV.UK sets out:
| Allowance | Amount |
|---|---|
| Personal Savings Allowance, basic rate taxpayer | £1,000 |
| Personal Savings Allowance, higher rate taxpayer | £500 |
| Personal Savings Allowance, additional rate taxpayer | £0 |
| Starting rate for savings | Up to £5,000, if other taxable income is below £17,570 |
The starting rate shrinks by £1 for every £1 of other income above your Personal Allowance. Interest above your allowances is taxed at your income tax rate, which reduces the compounding effect. Our guide to take home pay explains how the tax bands work.
ISAs: compounding without tax
Interest and growth inside an ISA aren't taxed, so the full return compounds. GOV.UK confirms that in the 2026 to 2027 tax year the most you can save in ISAs is £20,000. That allowance can be split across ISA types.
The Lifetime ISA lets you pay in up to £4,000 a year (counting towards the £20,000), with a 25% government bonus of up to £1,000 a year. Withdrawals for anything other than a first home, terminal illness or reaching 60 can carry a charge, so read the rules first.
Changes to cash ISAs from April 2027 were announced in the Autumn Budget 2025. NS&I says the cash ISA limit for savers under 65 will be £12,000 from 6 April 2027, within the overall £20,000. That doesn't affect the 2026/27 allowance, but it's worth knowing if you plan to use your cash ISA allowance in future years.
Inflation: the real return
Compounding works on prices too. The Bank of England explains that the government has set it a target of keeping inflation at 2%, measured by the Consumer Prices Index. If your savings earn less than inflation, the money buys less over time even though the balance grows.
The real return is: (1 + interest rate) ÷ (1 + inflation) − 1
At 4% interest and 2% inflation, the real return is about 1.96%. At 4% interest and 5% inflation, it's negative, around −0.95%. After tax, the real return falls further, which is one reason the ISA wrapper matters.
Compound interest on debt
The same maths works against you on borrowing. Interest added to a credit card or overdraft balance is charged interest itself next month. Mortgages and loans are calculated with a related formula; see how mortgage repayments are calculated and try the loan calculator. Paying off expensive debt often beats saving at a lower rate.
A savings checklist
- Compare accounts by AER, not gross rate.
- Check whether any bonus rate ends after a fixed period.
- Work out whether your interest will go over your Personal Savings Allowance.
- Use your ISA allowance for savings that would otherwise be taxed.
- Compare your rate with current inflation to see the real return.
- Set up regular deposits early, because time matters more than amount.
The percentage calculator is handy for quick rate comparisons, and the age calculator helps when a product depends on age limits, such as the Lifetime ISA's under-40 opening rule. Make It Flow builds these free tools so you can check numbers quickly. If you run an accounting firm and want to automate client reminders, talk to us.
FAQ
How does compound interest work?
Each time interest is paid, it's added to your balance, and future interest is calculated on the new, larger balance. Over time you earn interest on your interest as well as on your original money. The longer the money stays invested and the higher the rate, the bigger the effect.
What is the formula for compound interest?
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 added each year, and t is the number of years. Subtract P from A to get the interest earned.
What is the difference between AER and gross interest?
Gross is the stated rate before tax, without adjusting for how often interest is paid. AER shows what that rate would earn over a year if interest were compounded annually, so it accounts for monthly or quarterly payments. A 4% gross rate paid monthly is about 4.074% AER.
How much will £10,000 grow in 10 years?
At 4% compounded annually, about £14,802.44. Compounded monthly, about £14,908.33. At 3% yearly it would be about £13,439, and at 5% about £16,289. Tax and inflation reduce the real value, so check your allowances and compare the rate with inflation.
Is compound interest taxed?
Savings interest is taxable income, but most people have a Personal Savings Allowance of £1,000 (basic rate) or £500 (higher rate), and some also get the starting rate for savings of up to £5,000. Interest in an ISA is tax-free and doesn't count towards these allowances.
Does monthly compounding make a big difference?
It helps a little. On £10,000 at 4% for 10 years, monthly compounding earns about £106 more than yearly. Daily compounding adds only about £10 more than monthly. The interest rate and how long you save make a much bigger difference than the compounding frequency.
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