Compound interest

When you invest money, you receive interest. The special thing happens the following year: then not only your starting amount earns interest, but also the interest from before. A small head start grows into a big one over the years. This principle is called compound interest, and you find it wherever the increase is always based on the current amount: in a savings account just as in a growing population.

Interest on interest

You invest 100 euros at 5 % per year. In the first year you get 5 euros of interest, so you have 105 euros. In the second year, however, 5 % of 105 euros is calculated, which is 5.25 euros. The extra 25 cents are the interest on the interest. With simple interest you would get exactly 5 euros every year instead, because there only the 100 euros of starting capital ever earn interest.

The same factor every year

Instead of adding the interest separately each year, you multiply the capital by a fixed factor. At 5 % that is 1.05. After one year you have 1.05 times as much, after two years 1.05 times that again, so 1.05 times 1.05. This is how the growth chains together year after year.

Why waiting pays off

Because the number of years sits in the exponent, time has a far stronger effect than with simple interest, where the same amount is added every year. 200 euros at 10 % are $200 \cdot 1.1^2 = 242$ euros after two years. If an amount doubles yearly, that is 100 % growth, then 1000 euros become $1000 \cdot 2^3 = 8000$ euros after three years. The same calculation fits anywhere something gains the same percentage each year: a forest with 10 % more trees per year grows by exactly the same factor 1.1.