Savings
Put £100 in a savings account and leave it. Watch your interest start earning interest of its own, find out how much it matters when the bank adds it, then try your own numbers.
1 · £120 or £121?
Put £100 in a savings account paying 10% interest a year. We're using 10% to keep the maths simple.
After one year the bank adds £10 of interest, and you have £110.
Leave it another year. After two years, how much do you have?
It's £121. Most people say £120: £10 of interest, twice.
That extra £1 is compound interest. Most of what follows is that same pound, repeated.
2 · Your interest earns interest
In year two the bank pays 10% again. But this time it's 10% of £110, not £100, because last year's £10 is part of your balance now.
That gives you £11 in interest.
£10 of it comes from your original £100, just like year one.
The extra £1? That's 10% of last year's £10.
Your interest is now earning interest of its own.
3 · Slowly, then quickly
With simple interest you'd earn £10 every year, always worked out on your first £100: a staircase that reaches £200 after ten years.
Compound interest adds 10% of whatever is there: £11 in year two, £12.10 in year three, £13.31 in year four. Nothing new happens; the same step repeats on a slightly bigger pot.
By year ten your £100 earns £23.58 in a single year, and ends at £259 against £200.
your turn
4 · Does it matter when it's added?
If interest earns interest once it's in your account, getting it added sooner should help. Same £100, same 10%, but added every month: one-twelfth of the rate, 0.8333%, each month.
Month one: £100 × 0.8333% is about 83p, added straight away.
Month two: about 84p, because month one's 83p is in the balance now and earning too.
Keep going for twelve months and you have £110.47 instead of £110: 47p more, because your interest started earning sooner. It's small because each month's interest has only a few months to grow.
Savings accounts show this as two rates. The gross rate is the yearly rate before tax, without interest on interest: 10%. The AER (Annual Equivalent Rate) counts it: 10.47%.
So compare AER with AER. An account adding 10.47% once a year has the same AER, and leaves you the same £110.47 after a year, if the rate stays the same and you leave the interest in.
Some banks work interest out every day but add it only once a year. Worked out daily isn't added daily: it earns interest of its own only once it's added.
your turn
5 · The same idea at real rates
Try a more realistic 4%, close to the Bank of England's Bank Rate of 3.75% in September 2026. Your £100 earns £4 in year one and £4.16 in year two: that first £4 earning 16p.
Repeat that for 30 years and you have £324, against £220 with simple interest.
Make it 5% instead of 4%: £432. That one percentage point is worth another £108.
Or look at time. After 20 years you'd have £219; the last ten years add another £105, without a penny more from you.
And adding the interest monthly instead of yearly? £331: just £7 more over 30 years.
Time and the interest rate do most of the heavy lifting.
your turn
Rates fixed, nothing added, all interest left in, no tax or inflation. Monthly and yearly use the same gross rate.
6 · What slows it down
Compounding works best when you leave the interest in. Take it out and spend it, and that money can't earn interest of its own. A fund that pays its income out works the same way.
Tax can take a slice once your interest goes over your tax-free Personal Savings Allowance. ISAs protect eligible savings from UK tax.
And prices rise. If your money grows 4% but prices rise 2%, it buys only about 2% more.
Debt compounds the same way, against you. On high-interest debt such as many credit cards, unpaid interest gets charged interest too, and how often it's added matters far more.
That extra £1 is the whole of compound interest: last year's interest earning interest of its own.
Give it a good rate, time, and leave it in. How often it's added? The AER already counts it.
Compound interest only works for the money you leave in, at the rate you actually get. Three things to check on any savings account:
The gross rate leaves out interest on interest; the AER counts it. Two accounts with the same AER pay the same over a year, if the rate stays the same and you leave the interest in. Don't set one account's gross rate beside another's AER.
"Worked out daily" can still mean added once a year: look for when it's paid in. And if the interest is paid out to your current account and spent, it stops earning: you're back to simple interest.
Interest over your Personal Savings Allowance is taxed: £1,000 a year for basic-rate taxpayers, £500 for higher rate, £0 for additional rate (the starting rate for savings can add more on a low income). ISA interest is tax-free, up to £20,000 paid in for 2026 to 2027. And set the rate beside inflation: 4% while prices rise 2% buys only about 2% more.
Put in what you'd leave in an account, its rate and how long. See where the money comes from, what it buys in today's prices, and which change would help most.
what you'd have
£324after 30 years
Assumptions: one payment in at the start, nothing added or taken out, the rate fixed for the whole time and every penny of interest left in, no tax. A gross rate is split evenly: added monthly, each month adds the rate ÷ 12. Daily uses 365 days a year. An AER is grown once a year. Saving a little every month is a different sum, not covered here. Education, not financial advice.
The video
The same story, drawn: the jar where every coin sprouts a little coin, ten years of columns climbing past the simple-interest staircase, a coin for every month, and the jars at 4% for 30 years. Good for sending to anyone with a savings account they never look at.
How the numbers on this page are made. One model drives every drawing, readout and sentence. Interest added n times a year at a gross rate r: balance = £100 × (1 + r ÷ n)n × years. Simple interest: £100 × (1 + r × years). AER = (1 + r ÷ n)n − 1. The 10% in chapters 1 to 4 is illustrative. At 10% a year: £110, £121, £133.10, £146.41, £161.05 after five years, £259.37 after ten (£23.58 of interest in year ten), against £200 simple. Added monthly: 10% ÷ 12 = 0.8333% a month, 83p then 84p, £110.47 after a year, an AER of 10.47%. At 4%: £4, then £4.16; after 30 years £220 simple, £324.34 added yearly, £331.35 added monthly (+£7.01), £432.19 at 5% (+£107.85); after 20 years £219.11, so the last ten years add £105.23. Over ten years, adding monthly instead of yearly is worth £1.06 at 4% (£149.08 against £148.02) and £11.33 at 10% (£270.70 against £259.37). Real growth at 4% with prices rising 2%: 1.04 ÷ 1.02 − 1 = 1.96% a year. Daily uses 365 days, no leap years (it changes pennies).