Compound interest explained: how your savings really grow

With simple interest, £10,000 at 5% earns £500 a year, forever — after 20 years: £20,000.

With compound interest, year one’s £500 is added to the pot, so year two earns interest on £10,500, and so on. Each year’s growth is slightly bigger than the last:

Same rate, same deposit, same 20 years — 71% more interest, purely from reinvesting the growth. And the curve steepens with time: the final five years of those twenty generate more interest than the first ten.

For a lump sum:

A = P × (1 + r/n)^n×t

• P — the starting amount;
• r — the annual rate (as a decimal);
• n — how many times a year interest is added (12 for monthly);
• t — years.

Two things to notice. First, time is in the exponent — it’s the most powerful variable in the equation, which is the mathematical reason “start early” beats “save more, later”. Second, more frequent compounding helps a little (that’s why our monthly-compounded £10,000 beats the annually-compounded £26,533) — the calculator lets you switch frequency and see the difference. UK accounts quote AER precisely so you can compare rates fairly regardless of how often they compound.

Most people don’t invest lump sums — they save monthly. Here’s £200 a month at 5%:

Look at the shape, not just the totals: doubling the time from 10 to 20 years nearly trebles the pot; by year 30, growth (£94,452) has overtaken everything you contributed (£72,000). In the early years your contributions do the work; after enough time, compounding does.

Two savers put away £200 a month at 5% until age 65:

• Starts at 25 (40 years): pays in £96,000 → ends with £305,204
• Starts at 35 (30 years): pays in £72,000 → ends with £166,452

The early starter contributed just £24,000 more but finishes £138,752 ahead — the first decade’s contributions spend 30–40 years compounding, and that dwarfs everything else. If you take one action from this guide: start now, at whatever amount, and let time do the heavy lifting. (This is exactly why pension contributions in your twenties matter so much — see our retirement guide.)

• AER (annual equivalent rate) is the true annual rate including compounding — always compare savings accounts on AER, not the “gross” rate.
• Tax: the personal savings allowance makes the first £1,000 of interest tax-free for basic-rate taxpayers (£500 higher-rate, £0 additional-rate). Above it, interest is taxed as income — a 4% account effectively pays 2.4% to a higher-rate taxpayer.
• ISAs shelter interest and investment growth from tax entirely (£20,000 allowance a year) — over decades, protecting compounding from tax is worth far more than it looks.
• Chase the rate: at 3% instead of 5%, that 30-year £200-a-month pot is about £50,000 smaller. The rate you settle for is a six-figure decision over a saving lifetime — test the sensitivity in the calculator.

Compounding works on numbers; your life runs on purchasing power. If your savings earn 5% while inflation runs at 2%, your real return is roughly 3% — the pounds multiply faster than what they can buy. Two practical rules:

• For long-term goals, judge outcomes in today’s money — a projection at a “real” rate (rate minus expected inflation) is more honest than a nominal one;
• Cash that beats inflation is winning; cash below inflation is quietly shrinking, however satisfying the balance looks. That’s the argument for investing long-horizon money — accepting volatility in exchange for historically higher compounding rates.

Everything above also describes your debts — from the lender’s side. Credit card interest compounds monthly against you: a £3,000 balance at 24.9% repaid at the minimum costs £5,998 in interest over nearly 29 years — the same exponential maths, working for the bank. The order of operations follows directly: clear high-interest debt first (nothing you save at 4–5% outruns debt at 25%), then put compounding to work for you. Our minimum payments guide covers the escape route.