Guide · Savings & Investing
How Compound Interest Works (and Why Starting Early Changes Everything)
Compound interest turns modest, consistent saving into serious wealth — but only if you give it enough time. Here is the formula, the intuition, and the numbers that show why starting five years earlier is worth more than saving twice as much.
The formula
Compound interest has a simple formula that produces dramatically non-linear results over time:
Compound interest formula
A = P × (1 + r/n)^(n×t)
A = final amount · P = principal · r = annual rate · n = compounds per year · t = years
The exponent is what makes compound interest powerful. As t grows, the curve bends sharply upward. £10,000 at 7% for 10 years grows to £19,672. For 30 years, it becomes £76,123 — not triple the 10-year result but nearly four times it.
What £10,000 becomes over time
The impact of compound interest becomes clear when you hold the rate constant and vary the time horizon. Assuming a 7% annual return (roughly the long-run real return on a global equity index fund):
| Time period | Total value | Interest earned |
|---|---|---|
| 5 years | £14,026 | £4,026 |
| 10 years | £19,672 | £9,672 |
| 20 years | £38,697 | £28,697 |
| 30 years | £76,123 | £66,123 |
| 40 years | £149,745 | £139,745 |
No additional contributions. The same £10,000 grows nearly 15× in 40 years purely from compounding.
Why starting early beats saving more
Consider two investors. Alex starts at age 25 and invests £300/month until age 35, then stops. Sam starts at age 35 and invests £300/month all the way to age 65. Both assume 7% annual returns:
| Investor | Contributions | Total invested | Pot at 65 |
|---|---|---|---|
| Alex (starts 25, stops 35) | 120 months | £36,000 | £264,432 |
| Sam (starts 35, never stops) | 360 months | £108,000 | £340,513 |
Sam puts in three times as much money and still only ends up about 29% ahead — because Alex's money had 30 extra years to compound. Had Alex continued contributing from 35 to 65, the pot would reach £604,000. The lesson: time in the market is irreplaceable.
The Rule of 72
A quick mental shortcut: divide 72 by the annual return rate to find how many years your money takes to double.
At a 7% return, a £50,000 ISA doubles to £100,000 in about 10 years, then to £200,000 in 20, and £400,000 in 30 — without a single additional penny invested. This is why a strong equity allocation in your 20s and 30s matters so much: you have enough doublings ahead of you for the rate to dwarf the pound amounts you contribute.
Compounding in practice: savings accounts vs investments
Compound interest works in two contexts with very different outcomes:
- Cash savings accounts — Your bank compounds interest on your balance, typically monthly or annually. At today's rates (4–5% AER on easy-access accounts), this is meaningful for short-term goals. But cash loses to inflation over the long run.
- Investment accounts (ISA, SIPP) — Total returns (dividends reinvested, capital growth) compound over time. Historically 7–9% real annual return for a global equity portfolio. This is where long-term compound growth lives. Wrapping investments in an ISA or SIPP means the compounding is also tax-free.
- Debt — Compounding works against you with high-interest debt. A £3,000 credit card balance at 25% APR compounds to over £9,000 in 5 years if untouched. The same maths that builds wealth destroys it when you're on the wrong side.
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which is only calculated on the principal), compound interest grows exponentially over time because each period's interest becomes part of the base for the next period's calculation.
What is the Rule of 72?
The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6% annual return, your money doubles roughly every 12 years (72 ÷ 6 = 12). At 9%, it doubles every 8 years. The rule works best for rates between 4% and 12%.
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest. On £10,000 at 5% for 20 years: simple interest gives £10,000 profit (£20,000 total), but compound interest gives £16,533 profit (£26,533 total) — a 65% larger return from the same rate.
How often should interest compound?
More frequent compounding means slightly higher returns. Daily compounding beats monthly, which beats annual. In practice the difference is small — a 5% rate compounded daily gives 5.13% effective annual yield versus 5.0% compounded annually. For savings accounts, look for AER (Annual Equivalent Rate) which already accounts for compounding frequency.