Compound interest is famously powerful and famously boring for the first decade. Both facts come from the same equation.
Simple versus compound
Simple interest pays on the original principal only. Compound interest pays on the principal plus everything earned so far, so the base grows each period.
£10,000 at 5% for 20 years: simple interest returns £20,000. Compound interest, annually, returns £26,533. The extra £6,533 is entirely interest earning interest.
Over five years the two are close — £12,500 against £12,763. The gap only becomes dramatic with time, which is why compounding feels underwhelming when you start and unstoppable when you look back.
How much the frequency matters
The same nominal rate compounds to different amounts depending on how often it is applied. £10,000 at 5% for 10 years:
| Compounded | Periods/year | After 10 years | Effective rate |
|---|---|---|---|
| Annually | 1 | £16,289 | 5.000% |
| Semi-annually | 2 | £16,386 | 5.063% |
| Quarterly | 4 | £16,436 | 5.095% |
| Monthly | 12 | £16,470 | 5.116% |
| Daily | 365 | £16,487 | 5.127% |
| Continuously | ∞ | £16,487 | 5.127% |
Two things stand out. Monthly beats annual by a useful amount. And the curve flattens hard after that — daily is barely better than monthly, and continuous compounding, which sounds exotic, is worth almost nothing over daily. This is why "compounded daily" in an advertisement is close to meaningless.
The rule of 72, and where it breaks
Divide 72 by the rate to get the years to double. At 6%, 72 ÷ 6 = 12 years. The exact answer is 11.9, so the shortcut is good enough for mental arithmetic.
It holds well between about 4% and 12%. Outside that it drifts: at 2% the rule says 36 years and the truth is 35; at 20% it says 3.6 and the truth is 3.8.
The useful version is not the number but the shape. Doubling time is inversely proportional to rate, so an extra percentage point matters far more at low rates than at high ones. Going 2% to 3% cuts 12 years off the doubling time; going 10% to 11% cuts less than one.
Why starting early beats saving more
This is the result that changes behaviour, and it is worth seeing in numbers.
Two savers, both earning 7%. A saves £200 a month from 25 to 35, then stops and never adds another penny. B saves nothing until 35, then saves £200 a month until 65.
A contributed £24,000 over ten years. B contributed £72,000 over thirty. At 65, A has roughly £280,000 and B has roughly £244,000.
A paid in a third as much and finished ahead, because A's money had thirty extra years to compound. This is the entire argument for starting early, and it stops working the moment you delay — the years lost at the beginning are the most valuable ones.
Inflation, tax and the real return
A 7% return with 3% inflation is not 7%. It is about 3.9% in purchasing power, and that is the number that buys things.
The exact calculation is (1 + nominal) ÷ (1 + inflation) − 1, which gives 3.88% rather than the 4% you get by subtracting. The difference is small annually and compounds like everything else.
Tax comes off before that. An account taxed at 20% on gains turns a 7% nominal return into 5.6%, which against 3% inflation is 2.5% real. Tax-sheltered accounts are not a small optimisation — over thirty years the difference between 3.9% and 2.5% real is roughly double the final balance.
The same maths, working against you
Compounding is indifferent to which side you are on. Credit card debt at 22% APR compounds monthly against you at an effective 24.4%.
A £5,000 balance with minimum payments of 2% takes over 30 years to clear and costs roughly £13,000 in interest. The rule of 72 says the debt would double in three years if you paid nothing at all.
This is why paying down high-interest debt beats investing almost every time. A guaranteed 22% return by clearing a card is better than a hoped-for 7% in the market, and it is not close. The Loan Calculator shows what any balance actually costs over its life.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the years. For monthly compounding n is 12; for annual, n is 1.
Does compounding frequency matter much?
Monthly meaningfully beats annual — about 5.12% effective against 5.00% on a 5% nominal rate. Beyond monthly the gains almost vanish: daily is barely better, and continuous compounding is worth essentially nothing over daily. "Compounded daily" in an advert is close to meaningless.
What is the rule of 72?
Divide 72 by the interest rate to estimate the years for money to double. At 6% that is 12 years, against an exact 11.9. It is accurate between roughly 4% and 12% and drifts outside that range.
Is it better to start early or save more?
Start early, usually by a wide margin. Someone saving £200 a month from 25 to 35 and then stopping ends up ahead of someone saving the same from 35 to 65, despite contributing a third as much — because the early money compounds for thirty more years.
How do I account for inflation?
Divide rather than subtract: (1 + nominal) ÷ (1 + inflation) − 1. A 7% return with 3% inflation is a 3.88% real return, not 4%. Then take tax off before that, which is often the larger effect over long periods.
Should I invest or pay off debt first?
Almost always clear high-interest debt first. Compounding runs against you at the same speed it runs for you, and clearing a card at 22% is a guaranteed 22% return, against a hoped-for market return in single digits.