How does the saying "money breeds money" apply to simple interest?

The simple interest is calculated as the principle amount times the rate of interest times the number of years.

So, if our principle amount is $100 and rate is 5% and time is 1 year, then at the end of the year we will yield an interest of :

Hence, we will earn $5 over our initial amount of $100 making it $105 by the end of one year. Then next year again, we will get, making it by second year end and this chain continues.

In this way we can see that each year the initial amount is increasing with simple interest. So, this validates the sentence 'money breeds money' .