How does work compounding interest?

  Do you want to be a millionaire? Well, you could just try working really hard until you get paid a ton of money. Or you could use compounding interest to exponentially grow your money. But what even is it, and how does it work?

 Compound interest is just the principle of getting interest on previous interest. Say you invest $10,000 into a bank. If every month you got a 1% interest payment, after the first month you'd have invested $10,100 into that bank. The next month, the 1% interest would apply to the new $10,100 number, meaning your interest payment would be $101.00, bringing your total invested to 10, 1201 this cycle would continue with interest compounding in your subsequent interest payments getting larger and larger. Essentially compounding interest means the longer you invest in something, the more you get out of that investment exponentially. This can be incredibly useful to transform a little bit of money into a lot over time. So just how powerful is compounding interest in your quest to become a millionaire? 

Let's do some math. The formula looks like this and it's not as scary as it looks. A is the final amount. P is the initial principal balance or what you initially invest. R is the interest rate. N is the number of times that interest is applied over a period, let's say a year. So if it gets paid out per month that would be 12, or if it gets paid out each year that would be one. And T is the number of time periods. So if we're using years and we say 30 years, that would be 30. While this initially looks complicated. There's online calculators to make it very simple for you to do yourself without having to figure out this formula. Let's go ahead and figure out what it would mean if we took that $10,000 we were talking about before, invested it at a 3% annual rate of return or interest rate for 30 years, with interest being paid at the end of each year. If we just replace the letters with all the data, we would get something like this. Simplifying that out, it just becomes 10,000 * 1.03.l To the power of 30. If you calculate that at the end of the 30 years your initial 10,000 would become $24,272, you would more than double your money in that time period. Conversely, if you invested that 10,000 into a place that only gave you simple interest or interest that didn't compound, you'd get back 3% of the initial 10,000 per year, or $300.00 per year for 30 years, which only comes out to  $9000 in addition to that initial 10. That means with all things the same in this scenario other than simple versus compounding interest. With simple interest you'd only have $19,000 after 30 years, but with compounding you'd have 24,000. That's 26% more money using compounding interest. 

But how do you become a millionaire? Let's make these numbers a little bit larger to figure out what you'd need to invest over a 30 year period to get $1,000,000. Well, if you invest $231,500 with compounding interest, after 30 years that money would turn into $1,000,000 versus simple interest just leaving you with $578,000. The difference is crazy. Without compounding interest, you'd be out 400 grand. But at the end of the day you do still have to come up with that initial $231,000 number. All this comes down to simple math though and it's how financially savvy people use math to their advantage. It causes their interest payments to go up and up exponentially overtime. So when it comes to compounding interest, it really does pay to invest early and invest often.