What is compound interest?

Compound interest is a notion of financial mathematics well known to investors and bankers. Compound interest is when interest earned on a principal in a given period is reinvested with that principal in the next period to earn more interest. We are talking about compound interest as opposed to "simple" interest that is not reinvested.

The accumulation of wealth that results from this phenomenon is not linear (same amount of interest collected in each period) but exponential (a greater interest in each period). This exponential accumulation plays in favour of the investor taking advantage of it.

To illustrate compound interest, consider a person who invests 1.000€ at an interest rate of 10% per annum. He will receive 100€ in interest after one year. This will be invested the following year along with the initial capital, or 1.100€ in total, and these will generate 110€. The 1.210€ thus obtained will be reinvested again and will also generate 10% subsequently. After 10 years, this person will not have generated a profit of 100%, that is 10 times 10%, but a profit of 160%, thanks to the reinvestment of the interest collected each year which will also have generated interest.

When subject to compound interest, the principal in period t is calculated with the following formula:

Capital in period t
= Initial capital * (1 + interest rate) * (1 + interest rate) * .... * (1 + interest rate)
= Initial capital * (1 + interest rate) ^ t