How compound interest works, with a UK calculator
Compound interest means you earn interest on your interest. What the S&P 500 has really returned, the 2008 crash in dollars and pounds, what tax takes outside an ISA, and a calculator to try your own numbers.
HanaHow9 minute readCompound interest means your interest earns interest too. Each month’s growth stays in the pot, so the next month’s growth is worked out on a bigger total. You’ll hardly notice it in the first few years, but over 40 years it can be most of what you end up with.
How compound interest works
Put £100 somewhere that grows by 20% a year. After one year you have £120: the £100 you put in plus £20 of interest.
In the second year you earn 20% of £120, which is £24, so you finish the year with £144.
If you’d only earned interest on the original £100, you’d have £140. The extra £4 is interest on the first year’s interest. It’s a small amount, but next year you earn interest on that £4 as well, and the gap keeps widening.
£1 a year for 100 years
Pay £1 in at the start of every year for 100 years, and say it grows at 20% a year, added monthly. That’s 1.67% a month, which works out at about 21.9% over a whole year. You’ve paid in £100 in total. At the end you’d have £2,286,786,350, or about £2.3 billion.
Almost all of it turns up near the end:
- After 50 years you’d have £112,734.
- After 75 years, £16,056,469.
- After 99 years, £1,875,351,048.
Year 100 on its own adds £411,435,302, and 86% of the final amount arrives in the last ten years.
Twenty percent a year for a century isn’t realistic. At the S&P 500’s long-run 10.7% a year, the same £100 would grow to about £269,000.
What the S&P 500 has really returned
The S&P 500 is an index of 500 of America’s biggest listed companies. A committee at S&P Dow Jones Indices decides which companies are in it, using rules on size, trading and profits, so it isn’t strictly the 500 largest. It started in March 1957.
From 1957 to 2025, with dividends reinvested, it grew by 10.7% a year in dollars. That’s before fund charges and tax.
That 10.7% is an average. The years behind it swung a long way:
- The best year was 1958, up 43.4%.
- The worst was 2008, down 37.0%.
- 15 of the 69 years from 1957 to 2025 ended lower than they started.
It matters which average you use. The simple average of those yearly returns is 12.0%, but your money doesn’t earn the simple average. A 37% fall followed by a 26.5% rise, as in 2008 and 2009, averages to about −5% a year, yet $100 became $79.67, which is −10.7% a year. The 10.7% here is the compound rate, the one your money actually earned.
For a UK investor counting in pounds, the same years give 11.8% a year, because the pound fell against the dollar over that time. Currency can move the other way too.
After US inflation, the 10.7% comes to about 6.8% a year.
What an index fund is
An index fund, or tracker, buys every company in the index in proportion to its size. Nobody in the fund chooses which shares to buy. The biggest companies get the biggest slices: in late September 2026 the largest holdings were NVIDIA, Apple, Microsoft, Alphabet and Amazon, and the top ten made up nearly 40% of the index.
Paying a fund manager to pick shares hasn’t usually done better. In S&P’s SPIVA report for mid-2026, 92.6% of actively managed large US funds did worse than the S&P 500 over the 20 years to 30 June 2026.
A tracker isn’t a safe place for money. It owns the whole market, so when the market falls, the fund falls with it.
The 2008 crash, in dollars and pounds
Say you’d put $100,000 into the S&P 500 at its peak on 9 October 2007.
- A year later, on 9 October 2008, it was worth about $59,400.
- At the bottom on 9 March 2009 it was about $44,750, down 55%.
- It didn’t get back to $100,000 until April 2012.
- Left alone, with dividends reinvested, it was worth about $709,600 on 25 September 2026.
For a UK investor the fall was smaller, because the pound dropped against the dollar at the same time, from about $2.03 at the peak to $1.38 at the bottom. £100,000 invested at the peak fell to about £66,100, a drop of about a third. By 25 September 2026 it was worth about £1,088,800.
These are index figures before charges and tax. A real UK tracker, after its charges and the US tax taken from its dividends, would be a little lower, nearer £1.02 million.
Anyone who sold at the bottom locked in a loss of $55,250.
£200 a month from age 25
You don’t need £100,000. £200 a month from age 25 to 65, growing at 10% a year, comes to £1,110,070. You’d pay in £96,000, so over £1 million of that is growth. 10% is a bit under the S&P 500’s long-run average, and there’s no promise it’ll be repeated.
Start at 35 instead and you’d have £412,569 at 65. The extra ten years cost £24,000 in payments and add nearly £700,000 to the pot, because those early payments have the longest to grow.
The rate you assume changes the answer a lot over 40 years. £200 a month for 40 years:
- At 5% a year: £296,505
- At 7% a year: £494,308
- At 9% a year: £843,848
- At 10% a year: £1,110,070
Prices rise over 40 years too, so £1.11 million then won’t buy what £1.11 million buys now. With inflation at 2.5% a year, it would buy about what £413,000 buys today.
The calculator starts with the 10% example.
Compound interest calculator
Change any of the numbers and the results update. Leave the fee and inflation at 0 if you want to ignore them.
- Final value
- £1,110,070
- after 40 years
- Total paid in
- £96,000
- Growth
- £1,014,070
- In today’s money
- £413,424
- after 2.5% inflation a year
Show the figures for each year
| Year | Paid in | Growth | Value |
|---|---|---|---|
| 1 | £2,400 | £108 | £2,508 |
| 2 | £4,800 | £467 | £5,267 |
| 3 | £7,200 | £1,102 | £8,302 |
| 4 | £9,600 | £2,040 | £11,640 |
| 5 | £12,000 | £3,312 | £15,312 |
| 6 | £14,400 | £4,952 | £19,352 |
| 7 | £16,800 | £6,995 | £23,795 |
| 8 | £19,200 | £9,482 | £28,682 |
| 9 | £21,600 | £12,459 | £34,059 |
| 10 | £24,000 | £15,973 | £39,973 |
| 11 | £26,400 | £20,078 | £46,478 |
| 12 | £28,800 | £24,834 | £53,634 |
| 13 | £31,200 | £30,306 | £61,506 |
| 14 | £33,600 | £36,564 | £70,164 |
| 15 | £36,000 | £43,689 | £79,689 |
| 16 | £38,400 | £51,766 | £90,166 |
| 17 | £40,800 | £60,890 | £101,690 |
| 18 | £43,200 | £71,168 | £114,368 |
| 19 | £45,600 | £82,712 | £128,312 |
| 20 | £48,000 | £95,652 | £143,652 |
| 21 | £50,400 | £110,125 | £160,525 |
| 22 | £52,800 | £126,286 | £179,086 |
| 23 | £55,200 | £144,302 | £199,502 |
| 24 | £57,600 | £164,361 | £221,961 |
| 25 | £60,000 | £186,665 | £246,665 |
| 26 | £62,400 | £211,440 | £273,840 |
| 27 | £64,800 | £238,932 | £303,732 |
| 28 | £67,200 | £269,413 | £336,613 |
| 29 | £69,600 | £303,182 | £372,782 |
| 30 | £72,000 | £340,569 | £412,569 |
| 31 | £74,400 | £381,934 | £456,334 |
| 32 | £76,800 | £427,675 | £504,475 |
| 33 | £79,200 | £478,231 | £557,431 |
| 34 | £81,600 | £534,082 | £615,682 |
| 35 | £84,000 | £595,758 | £679,758 |
| 36 | £86,400 | £663,842 | £750,242 |
| 37 | £88,800 | £738,974 | £827,774 |
| 38 | £91,200 | £821,860 | £913,060 |
| 39 | £93,600 | £913,274 | £1,006,874 |
| 40 | £96,000 | £1,014,070 | £1,110,070 |
Growth is added monthly at the yearly rate you enter, and each payment goes in at the end of the month. The fee comes off the growth rate, so 7% with a 1% fee grows at 6%. Your monthly payment stays the same throughout. Today’s money is the final value scaled back by inflation, to show what it would buy at today’s prices. Real returns change from year to year; this uses the same rate every year.
Tax in the UK, and why an ISA matters
Outside an ISA, you pay Capital Gains Tax when you sell investments for more than you paid. In the 2026 to 2027 tax year the rate is 18% on gains that fit inside your unused basic rate band and 24% on the rest, after a £3,000 tax-free allowance. Higher and additional rate taxpayers pay 24%. GOV.UK lists the current rates.
On the £1,110,070 pot, the profit is £1,014,070. Sell it all in one tax year as a higher rate taxpayer and, after the £3,000 allowance, 24% comes to £242,657. Most people sell over several years and use a new allowance each time, so treat that as the top end. You’d also have paid tax on dividends along the way, above a £500 allowance, at 10.75%, 35.75% or 39.35% depending on your income.
The rates change
The Chancellor can change these rates at any Budget.
- Until 29 October 2024, the rates on shares were 10% and 20%. At the Budget on 30 October 2024 they rose to 18% and 24%, for sales made from that same day.
- The tax-free allowance was £12,300 until April 2023. It was cut to £6,000 for 2023 to 2024, then to £3,000 from April 2024.
The next Budget is on 28 October 2026, so check the rates on GOV.UK before relying on the figures here. HMRC keeps a table of past rates and allowances.
Inside a stocks and shares ISA
You don’t pay tax on interest, dividends or capital gains inside an ISA, and you don’t need to put any of it on a tax return. In the 2026 to 2027 tax year you can pay up to £20,000 into ISAs, in one account or split across several. £200 a month is £2,400 a year, well inside that. GOV.UK explains how ISAs work.
An ISA protects you from UK tax, not US tax. The US keeps 15% of the dividends paid by US companies before they reach an S&P 500 fund, and holding the fund in an ISA doesn’t get that back.
From 6 April 2027, the most you can put into a cash ISA each year drops to £12,000 if you’re under 65. The overall £20,000 limit stays, so the rest can go into other ISAs, such as a stocks and shares ISA. If you’re 65 or over, you can still put up to £20,000 a year into cash. GOV.UK has the details of the cash ISA change.
Tax in the US
In the US, gains on investments held for more than a year are taxed at 0%, 15% or 20%, depending on your taxable income. People with income above $200,000 ($250,000 for a married couple filing jointly) pay another 3.8%, so the top federal rate is 23.8%. Most states add their own tax. The IRS explains capital gains rates.
Congress sets these rates and has changed them often. The top rate on long-term gains was 28% from 1987, 20% from 1997, 15% from 2003 and 23.8% from 2013.
The nearest thing to an ISA is a Roth account. You pay in from money that’s already been taxed, and qualified withdrawals in retirement, growth included, are tax-free. In 2026 you can put up to $7,500 into IRAs (a Roth IRA counts towards that) and up to $24,500 into a 401(k), which can be a Roth 401(k) if your employer offers one. Roth IRAs have income limits; Roth 401(k)s don’t. The IRS compares the Roth accounts.
Fees compound too
Money taken in fees stops growing, so fees compound the same way returns do. Big S&P 500 trackers sold in the UK charge around 0.07% a year, and US ones as little as 0.03%. Here’s what paying 1% a year instead would cost.
On £200 a month for 40 years at 10%:
- With a 0.07% yearly charge you’d have £1,088,831.
- With a 1% yearly charge you’d have £843,848.
That 1% costs you £244,983, more than two and a half times the £96,000 you paid in.
Risks and assumptions
This guide explains how compound interest works. It isn’t financial advice and doesn’t take your circumstances into account. For advice on your own situation, speak to a regulated financial adviser.
Investments can go down as well as up, and you could get back less than you put in. The S&P 500 more than halved in dollars between 2007 and 2009.
The 10% used here is an assumption, not a promise. Real returns change from year to year, and in some years they’re negative. The calculator uses the same rate every year, so treat its results as an illustration.
The S&P 500 figures are S&P 500 total returns with dividends reinvested, before fund charges and tax, up to 25 September 2026. UK tax figures are for the 2026 to 2027 tax year and US figures for 2026.
Read the video transcript
£1 a year, for 100 years. What's it worth at the end? Not a hundred quid. At 20% a year, added monthly, that's about £2.3 billion. From £100 paid in. Every month, the interest earns interest. After 50 years it's only £112,000. Then it snowballs. Year 100 alone adds £411 million. 20%'s a fantasy, though. For a real number, people use the S&P 500. That's 500 of America's biggest companies. Since 1957, it's grown about 10.7% a year. But that's an average. It's been up 43% in one year, and down 37 in another. 15 years out of 69 went backwards. 10.7 is what's left once you smooth all that out. And nobody's picking the winners. An index fund just buys all 500, the big ones in bigger slices. Over 20 years, 9 in 10 professional stock pickers did worse than that. It's not a safe place, though. It's the whole market, and it is what it is. Here's what that means. $100,000 in at the top, October 2007. A year later, $59,000. By March 2009, about $45,000. More than half, gone. This is where people panic and sell. If you'd left it alone, it's now worth about $700,000. In pounds it only fell by a third, because the pound fell too. £100,000 then is over a million now. You don't need a hundred grand, though. 200 a month, pounds or dollars, at 10%, a bit under the average. From 25, that's about £1.1 million by 65, from £96,000 paid in. Start at 35, and it's about £400,000. Right. Here's the bit most people skip. In the UK, if it's not in an ISA, you pay Capital Gains Tax when you sell. Right now that's 18% or 24% of the profit, after the first £3,000. On that million, about £240,000. And that rate isn't fixed. The Chancellor changes it whenever the government wants. It was 10% and 20% until October 2024, then it went up the day it was announced. The tax-free part was £12,300. Now it's £3,000. Inside a stocks and shares ISA, none of that applies. No tax on the growth or the dividends, and nothing to declare. You can put in up to £20,000 a year. In the US, long-term gains are taxed at 0%, 15% or 20%, plus 3.8% for high earners, and Congress changes that too. The nearest thing to an ISA is a Roth account, like a Roth IRA or a Roth 401(k). It's taxed going in, then comes out tax-free in retirement. Last thing: fees compound too. Trackers charge under a tenth of a percent. Pay 1% instead, and it costs you about a quarter of a million. It can fall by half, and this isn't financial advice. That's HanaHow. See you next time.
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