Compound interest

When your money earns something, what it earns is added to the original sum. Next time you are earning on a larger base and then on a larger one still. At first it looks unremarkable, but after years the growth speeds up noticeably.

That is precisely the difference from simple interest, where the interest is always calculated on the original sum and the growth is therefore even.

How it works

At the end of each interest period the bank credits interest calculated on the current balance. That raises the balance, so the next period is calculated on a higher base.

Two things therefore matter: how long you leave the money to work and how often the interest is credited. Time is the stronger lever of the two: the first years seem dull, but they are exactly what drives the later growth.

The formula

$$A = P\left(1 + \frac{r}{n}\right)^{n \cdot t}$$

Each symbol has a simple meaning:

• $A$: the amount at the end of the period
• $P$: the initial investment
• $r$: the annual interest rate as a decimal (0.08 for 8%)
• $n$: how many times a year the interest is credited
• $t$: the number of years

The exponent in the formula is the mathematical expression of the fact that interest is calculated on an amount that has already earned interest. The factor $(1 + r/n)$ is applied as many times as there are periods.

A worked example

You put in €10,000 and add €200 every month. At an average return of 8% a year with monthly crediting you will have roughly €167,072 in 20 years.

Out of your own pocket you will have contributed only €58,000: the remaining €109,000 or so was earned by interest. What was earned thus exceeds what was put in.

What to watch out for

The interest rate is entered in percent, not as a decimal: 8 means 8%, not 800%. When comparing products with different crediting frequencies, use the effective interest rate, otherwise you will not be comparing like with like.

The calculation also excludes tax on gains and management fees. A one percent annual fee can carve off a substantial part of the return over three decades.

Where you will use it

Compound interest lies behind long-term investing, saving for retirement and the growth of credit card debt alike: it works in both directions. The same mathematics in reverse is called discounting.

Try your own figures in the compound interest calculator, which also shows a year-by-year breakdown and a growth chart.