Compound interest: how money grows on its own growth

Compound interest means earning a return not only on the money you put in, but also on the returns it has already earned. Each year’s growth becomes part of the base for the next year. Over short periods the effect is small; over decades it becomes the biggest part of the result.

A worked example

Take €10,000 earning a steady 5% a year, with every gain left in place. (Real investments rarely grow at a fixed rate; the steady figure just makes the arithmetic clear.)

• Year 1: 5% of €10,000 is €500, so you have €10,500.
• Year 2: 5% of €10,500 is €525, so you have €11,025.
• Year 3: 5% of €11,025 is €551.25, so you have €11,576.25.

The yearly gain keeps rising (€500, then €525, then €551.25) even though the rate stays at 5%. That growing gain is compounding. Carry on and the numbers look like this:

After	Simple interest (5% of €10,000 each year)	Compound interest (5% on the growing total)
10 years	€15,000	€16,289
20 years	€20,000	€26,533
30 years	€25,000	€43,219

With simple interest, paid only on the original €10,000, you gain the same €500 every year. With compounding, the total after 30 years is more than four times the starting amount, and more than half of the €33,219 gained is growth on earlier growth.

The rule of 72

A quick way to sense compounding is the rule of 72: divide 72 by the yearly percentage return to get roughly how many years it takes for money to double.

• At 4% a year: 72 ÷ 4 = about 18 years.
• At 6% a year: 72 ÷ 6 = about 12 years.
• At 9% a year: 72 ÷ 9 = about 8 years.

It is a rule of thumb, not an exact formula, but it is close for everyday rates. At 5%, it gives 14.4 years; the exact answer is about 14.2.

Why time matters most

In the example, the first ten years add about €6,300, while the third ten years add almost €16,700, at the same 5% rate. The longer money compounds, the more each year adds. This is why time spent invested tends to matter more than small differences in the starting amount. It also works in reverse on debt: unpaid interest on a loan or credit card compounds against you in the same way.

What works against it

Compounding applies to everything that grows or shrinks by a percentage each year, including costs.

• Fees. A yearly fee is taken from the total every year, so it compounds too. Shaving the return from 5% to 4% a year turns €26,533 after 20 years into €21,911. See investment costs for a full example.
• Inflation. Rising prices shrink what money buys. After 20 years at 5%, €26,533 sounds like a lot, but with inflation at 2% a year it buys only about what €17,856 buys today. The gain that matters is the real return: the return after inflation.
• Losses. Returns from shares and funds go up and down, and a bad year shrinks the base that future growth builds on. See risk and return.

Want to try your own numbers? Try the calculator, and compare the effect of prices with the inflation calculator.