Euler’s number (e) and an understanding of its not-so-obvious relationship with continuous growth has eluded so many of us, it’s only apt that we take some time out of our daily lives to sit down and have a little chat.
Interest earned on an investment of $100 @ 10% annual interest-rate is $100 a year. Usually, this $10 will be paid out at the end of the year. This can be modeled as:
If you don’t want to wait for one whole year to earn interest, you may ask for the accrued interest to be paid every six months. In that case, you earn $5 twice a year.
Following this logic, interest could be earned as frequently as desired while the total interest earned in a year remains the same. For example, you could demand 100 interest payments to be made at equal intervals of time within a year, net interest earned still being $10 per annum.
Okay, so now you’re getting 100 interest payments a year. By the end of the year, you’re able to add 10% to your investment.
You’re happy with the way things are until a friend shows up who tells you there’s a way to make more money, and it’s by re-investing the interest earned! Between each interest payment, you add the previously earned interest to the principal amount, thus changing the interest that will be earned next. Unlike previous scheme, the amount of interest paid keeps increasing. In the case of 100 interest payments, this can be modeled by:
To be continued…