Compound interest, fees and the maths of long-term saving

Compound interest is one of the few ideas in personal finance that is both simple and genuinely important. It explains why saving early matters so much, why small fees do so much damage and why the last decade of a savings plan produces more growth than the first two combined.

How compounding works

Simple interest pays a fixed amount on the original sum each period. Compound interest pays interest on the original sum plus all the interest already earned. The difference is negligible over a year and enormous over thirty.

Take 10,000 growing at 6 per cent a year. After one year it is 10,600. After ten years, it is about 17,900. After twenty, about 32,100. After thirty, about 57,400. The growth in the third decade, roughly 25,000, is larger than the growth in the first two decades combined. That is because the interest in later years is being earned on a much larger base.

A useful shortcut is the rule of 72: dividing 72 by the annual return gives the approximate number of years for money to double. At 6 per cent, that is about twelve years. At 3 per cent, twenty-four.

Why fees matter so much

A fee charged as a percentage of assets reduces the compounding rate directly. A fund that earns 6 per cent before fees and charges 1 per cent delivers 5 per cent. That sounds like a sixth of the return, and over one year it is. Over thirty years, the 5 per cent investor ends with about 43,200 from a 10,000 start, against 57,400 at 6 per cent. The fee has consumed roughly a quarter of the final sum.

The reason is that the fee is not just taken once. It is taken every year, and the money taken in year one would itself have compounded for twenty-nine more years. Fees compound against you in the same way returns compound for you.

This applies to any recurring percentage cost: fund charges, platform fees, advice fees and the trading costs inside a fund. It is why comparing total costs, not just headline fees, is worth the effort, and why a difference that looks trivial in a single year is not trivial over a working life.

Time versus amount

The compounding effect makes timing more powerful than most people expect. Someone who saves a fixed amount each year from age 25 to 35 and then stops will, at a steady 7 per cent, end up with more at 65 than someone who saves the same annual amount from 35 to 65. Ten years of contributions beat thirty, because the early contributions have three extra decades to grow. At lower returns the two end up close to level, which still means ten years of saving did the work of thirty.

The practical lesson is not that later saving is pointless, but that the cost of delay is higher than it feels. Each year of postponement removes the year with the most growth potential, the last one.

Inflation and real returns

Prices compound too. At 2 per cent inflation, the purchasing power of money halves in about 35 years; at 4 per cent, in about 18. What matters for a saver is the real return, the nominal return minus inflation. A savings account paying 3 per cent when inflation is 4 per cent is losing purchasing power, even though the balance is rising.

Long-term projections should therefore be made in real terms. A 6 per cent nominal return with 2 per cent inflation is a 4 per cent real return, and the rule of 72 says purchasing power doubles every 18 years rather than every 12.

Putting it together

The arithmetic points to a few principles. Start as early as possible. Keep recurring costs low. Expect most of the growth to come late, and do not be discouraged by slow progress in the early years. And measure progress against inflation, not against the nominal balance.

None of this tells you what to invest in, and it is not advice. It is the arithmetic that any saving plan operates under, regardless of the choices made within it.