What is interesting about compounding interests is that you get not only on you initial deposit, called principal, but also on the interest you get every year.

Usually, it compounds continuously but we would assume, that it is compounding annually.

So, if you take the actual interest rates on regulated deposits in France, that’s 1,25% per year. Let’s assume that you have 100€, so you will get 100+ 100(0,0125), for two years it’s 100+ 100 (0,0125) ^{2};, or for n years : 100 + 100 (0,0125) ^{n}. It’s not easy to calculate.

But how solve this question ? How long does it take to get a certain amount of money, given your principal deposit and the interest rate ? Woooh. This is where the log (logarithm) function is useful. So let’s put this following equation ….

100(0.0125) ^{x}; = 200

How to calculate “x” ?

First we need to simplify :

1(0.0125) ^{x} = 2 or

0.0125 ^{x}=2

x = log _{0,0125} 2

Let’s enjoy here the original video …