I have read from many financial experts that compound Interest is one of the fundamentals of wealth building. Some even call it the “Eighth wonder of the world”. Seriously? Some financial topic that is taught in college is considered the “Eighth wonder of the world”? What is it so magic about compound interest that people are willing to put right next to the Eiffel Tower?  Understanding compound interest is one thing (you will find it in any entry-level college textbook), But the real question is how to use it in your daily life and how to fight with it in your daily life. That’s right, fight (Well, not literally). Whether you realize it or not, compound interest is in our daily life sometimes it’s helping us increase the equity in our house and sometimes it is working against us eating away our wealth. 

To understand the ‘magic’ of compound interest. It would make sense to start with a textbook definition and play with different scenarios. Compound Interest is defined as “Interest on Interest”. The formula for compound Interest is as follows

Compound Interest Formula

A = P(1+r/n)^nt

^Where

            A = Amount

            P = Principal amount

            r = Interest Rate

            n = number of times interest is compounded per year

            t = time in years

Now that we know the formula let’s play with it.  I have put together a few Scenarios where you can play with different parameters and observe the input and outputs.

Let’s start with a few values. Let’s say we started with 100$ in savings. With 5% interest rate. It is compounded only 1 time per year and we put that away for 10 years. Here is what the result looks like.

Principal	100
r(Interest rate)	0.05
n(number of times compounded per year)	1
t(time in years)	10
Amount	162.8894627

Double the interest rate

In this scenario, we double the interest rate. The interest rate increased from 5 to 10 %. Here is what the result looks like.

Principal	100
r(Interest)	0.1
n(number of times compounded per year)	1
t(time in years)	10
Amount	259.374246

One might look at these results and say isn’t it obvious? Increasing the interest rate would increase the resulting amount. Well, sure that’s only one way of increasing the amount.

Double the number of years invested

Principal	100
r(Interest)	0.05
n(number of times compounded per year)	1
t(time in years)	20
Amount	265.3297705

In this scenario interest rate, and principal remain the same. But just by doubling the number of years the resulting amount surpassed more than scenario 2 which is double the interest rate. So all those risky investments that you make for 1-2% (even double) can be surpassed just by investing in safe investments for a longer period. So “starting early” is very important

Double the Principal

Principal	200
r(Interest)	0.05
n(number of times compounded per year)	1
t(time in years)	10
Amount	325.7789254

In this scenario, the initial investment amount is doubled. Interest rate and number of years stay the same.  One can observe that the resulting amount is much higher. This leads to another conclusion that You can beat higher interest rates just by saving more.

Conclusion

Although, we went through a few different scenarios. We did not fully explore the ‘magic’ of compounding. I don’t want to be a judge of whether compound interest is “Eigth wonder of the world”. But, it sure is very interesting. One another conclusion we did get to by playing with the above scenarios is this. You can out-earn an investment with a high interest rate just by saving more and investing for a longer period. So, ‘start early and save more’ will outearn all crazy investments that promise extraordinary returns.