Compound interest, the only free lunch

Every long-term investment return, in the end, is the same trick performed patiently: money earns a return, and then that return earns a return. It sounds trivial. It is the most powerful force most people never learn to use, because human intuition is stubbornly linear and compounding is not.

What compounding actually is

Simple interest pays you on your original stake, and only on your original stake. Put £1,000 in at 7% and you get £70 a year, every year, forever. After thirty years you have £1,000 plus thirty lots of £70, which is £3,100.

Compound interest pays you on your stake and on all the interest you have already earned. That second clause is the whole thing. Your interest starts earning interest. That interest then earns interest. After thirty years at the same 7%, your £1,000 has become £7,612.

The difference between £3,100 and £7,612 is not an accounting quirk. It is what happens when a process feeds on its own output. Drag the years slider below and watch the curve: for the first decade it looks almost like a straight line. It is in the last third that it detaches from the ground.

Why starting late is so expensive

Because compounding is exponential, the years at the end are worth far more than the years at the beginning. This produces a result that feels wrong the first time you meet it.

Anna invests £200 a month from age 25 to 35, then stops completely and never adds another penny. Ben starts at 35 and invests £200 a month until he is 65. Ben puts in three times more money over three times as many years. At 7%, Anna still ends up ahead.

Anna bought time. Ben bought the same asset, but he bought it late, and time is the one input you cannot buy back.

The rule of 72

You do not need a calculator to know how long money takes to double. Divide 72 by the annual return, and you have it, near enough.

• At 2% (a decent savings account), money doubles in about 36 years.
• At 7% (a long-run stock market average), it doubles in about 10 years.
• At 10%, in about 7 years.

Notice what happened there. Going from 2% to 7% did not make you three and a half times richer. Over forty years it makes you roughly six times richer, because each doubling multiplies everything that came before. Small differences in rate become enormous differences in outcome, given enough time.

The catch nobody mentions

Compounding needs two things: a positive return, and time undisturbed. It is fragile to interruption. Sell in a panic and you reset the clock. Take the money out to fund something else and you amputate the tail of the curve, which is the part that was about to do all the work.

This is why the boring advice is the correct advice. Not because patience is virtuous, but because the arithmetic rewards it disproportionately.