How to Calculate Compound Interest (UK ISA and Savings Examples)

What Compound Interest Actually Is, in One Paragraph

Compound interest is interest paid on interest. When your savings earn interest in year one and that interest is left to earn more interest in year two, the balance grows faster every year. The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the starting balance, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years. £10,000 saved at 4.5% for 25 years compounded monthly grows to £30,772, with £20,772 of that being interest. The free Compound Interest Calculator on ToolsForTasks does the maths instantly, including monthly contributions, and shows the breakdown year by year.

At a Glance

• The formula: A = P(1 + r/n)^(nt)

• £10,000 at 4.5% for 25 years grows to £30,772 (vs £21,500 at simple interest)

• Monthly compounding earns slightly more than annual compounding at the same rate

• A Cash ISA gets the tax-free version of the same growth

• Time matters more than rate: 30 years at 4% beats 20 years at 6% on most starting balances

The Compound Interest Formula

The standard formula is:

A = P(1 + r/n)^(nt)

Where:

• A = the final amount including interest

• P = the principal (starting balance)

• r = the annual interest rate as a decimal (4.5% = 0.045)

• n = the number of times interest is compounded per year

• t = the number of years

For most UK Cash ISAs and savings accounts, n = 12 (monthly compounding). For a fixed-rate bond it might be n = 1 (annual). For investment products it's effectively n = ∞ (continuous), though the difference between monthly and continuous is small at normal rates.

A Worked Example: £10,000 in a Cash ISA at 4.5%

Plug the numbers in:

• P = £10,000

• r = 0.045 (4.5%)

• n = 12 (monthly compounding)

• t = 25 (25 years)

A = 10,000 × (1 + 0.045/12)^(12 × 25)

A = 10,000 × (1.00375)^300

A = 10,000 × 3.0772

A = £30,772

That's £20,772 of interest on a £10,000 starting balance. By comparison, simple interest at the same rate over the same period would pay £11,250 (£10,000 × 0.045 × 25), so compounding adds £9,522. The longer the time horizon, the bigger the gap.

Compound Interest with Monthly Contributions

Most people don't deposit one lump and walk away. They contribute monthly, which compounds the contributions too. The formula gets more complicated, but the Compound Interest Calculator handles it instantly.

A worked example. Saving £200 a month into an ISA at 4.5% for 25 years, starting from £0:

• Total deposited: £60,000 (£200 × 12 × 25)

• Final balance: £119,143

• Interest earned: £59,143

Doubling your money in 25 years on £200/month is achievable in any normal interest rate environment. A Manchester graphic designer who started a Lifetime ISA at 24 and contributed the maximum £4,000/year for 14 years (the LISA cap stops at 50) saw her balance hit £92,000 by age 38, of which £36,800 was contributions, £8,400 was the 25% government top-up, and the rest was interest and growth.

Cash ISA vs Stocks and Shares ISA Compounding

Both compound the same way mathematically. The differences are the rate and the volatility.

Cash ISA. Interest rate fixed or variable, typically 3-5% in 2026. Capital is protected (FSCS up to £85,000). Returns are predictable. The compound interest formula gives an exact answer.

Stocks and Shares ISA. Returns come from a mix of dividends, capital growth, and reinvested distributions. Long-term returns from a global index fund have averaged around 7% nominal, 5% real (after inflation). Short-term returns can be heavily negative. The compound interest formula approximates long-term returns but doesn't capture the year-to-year volatility.

For a 25-year horizon, even a single year of -30% return early on can be recovered. For a 5-year horizon, a stocks ISA can lose money. Match the product to the time horizon.

How Compounding Frequency Changes the Maths

The same nominal rate compounds slightly differently depending on how often interest is paid.

Monthly compounding earns about 0.09 percentage points more than annual at a 4.5% nominal rate. On £10,000 over 25 years, that's a difference of about £700. Worth noticing, not worth chasing.

When you compare savings products, compare the AER (Annual Equivalent Rate). AER already accounts for compounding frequency and lets you compare like for like.

Time Beats Rate (Almost Always)

A common mistake is to obsess over getting the highest possible interest rate. Time matters more.

Compare two savers with £10,000 starting balance:

• Saver A earns 6% for 20 years: ends with £32,071

• Saver B earns 4% for 30 years: ends with £32,434

Saver B has a worse rate but more time, and ends up slightly ahead. This is why starting an ISA at 25 vs 35 makes more difference than picking the absolutely best ISA rate at age 35.

The "rule of 72" is a useful shortcut: 72 divided by the interest rate gives the number of years it takes for money to roughly double. At 6%, money doubles every 12 years. At 4%, every 18 years. At 3%, every 24 years.

How to Use the Compound Interest Calculator

The free Compound Interest Calculator on ToolsForTasks handles all the maths and shows the result year by year:

1. Enter the starting balance (the lump you have now)

2. Enter the interest rate (use AER if comparing savings products)

3. Enter the time horizon in years

4. Pick the compounding frequency (monthly is most common in the UK)

5. Optionally add monthly or yearly contributions

The output shows the final balance, total interest earned, and a year-by-year chart. The chart makes the curve obvious - growth is slow for the first 5-10 years, then accelerates. This is why people who give up on saving after a few years feel like compounding doesn't work; they didn't wait long enough.

Inflation: The Number You Actually Care About

Compound interest grows the nominal balance, but what matters is purchasing power. UK inflation has averaged around 2.5% over the last 30 years (with spikes much higher).

Your real return is approximately the nominal return minus inflation:

• 4.5% nominal - 2.5% inflation = 2.0% real return

• £10,000 at 2% real for 25 years = £16,406 in today's money

That's still positive, but it's less impressive than the nominal £30,772. When you set a savings goal, work backwards from how much spending power you want at the end and use a real rate (nominal minus inflation) to plan.

Common Mistakes

Confusing AER with the headline rate. Banks sometimes advertise the gross rate. AER is the apples-to-apples comparison.

Forgetting tax outside an ISA. Interest on a regular savings account is taxable above the £1,000 personal savings allowance (£500 for higher-rate taxpayers, £0 for additional rate). ISAs are tax-free.

Withdrawing and re-depositing. Once you take money out of a Cash ISA, you can sometimes re-deposit within the same tax year (a "flexible ISA"), but not always. Check before you withdraw.

Picking a one-year fixed rate at 5% over a five-year fix at 4.5%. The 5% looks better, but you'll need to find another 5% rate when the fix matures, which may not be available. The 4.5% locks in five years of compounding at a known rate.

Stopping monthly contributions during a bad year. In a Stocks and Shares ISA, continuing contributions during a downturn means buying units at lower prices, which improves long-term return. Stopping locks in the loss.

Frequently Asked Questions

What is compound interest in simple terms?

Interest paid on interest. Year one earns interest on the original balance. Year two earns interest on the original balance plus year one's interest. Year three earns interest on all of that. Over decades, the snowball effect adds tens of thousands of pounds to a typical savings pot.

How do I calculate compound interest on £10,000?

Use the formula A = P(1 + r/n)^(nt). At 4.5% compounded monthly for 25 years, £10,000 grows to £30,772. The free Compound Interest Calculator does the maths instantly for any starting balance, rate, time, and contribution schedule.

Is compound interest taxable in the UK?

Inside an ISA, no. Outside an ISA, interest is taxable above your personal savings allowance (£1,000 for basic rate taxpayers, £500 for higher rate, £0 for additional rate). Most everyday savers stay under the allowance, but high earners with large balances should compare ISA vs taxable accounts.

What's better, a Cash ISA or a Stocks and Shares ISA?

Cash for short-term goals (under 5 years), stocks for long-term goals (10+ years). For 5-10 years it depends on risk tolerance. Both compound the same way; stocks have a higher expected return and higher short-term volatility.

How does the Lifetime ISA bonus interact with compounding?

The 25% government bonus is paid monthly on your contributions. That bonus then compounds with the rest of your balance. Over decades, the bonus alone can compound to a significant chunk of the final balance.

What's the difference between APR and AER?

APR is for borrowing (mortgages, credit cards). AER is for saving. AER includes compounding effects so you can compare savings products on a like-for-like basis. Always compare savings using AER.

Final Thoughts

Compound interest is the closest thing to free money in personal finance, but only if you give it time. £200 a month into an ISA at a realistic 4.5% turns into £119,000 over 25 years. Skip the first 10 years and the same contribution pattern only reaches £29,000.

Start by running your numbers through the Compound Interest Calculator. If you're saving for a house deposit, the Mortgage Calculator and Stamp Duty Calculator will show you what the deposit needs to cover. Browse the free directory of financial tools for the rest.