# Compound Interest Definition – The Magic Formula to Wealth?

One of the most, if not the most, important formula for growing wealth right here.  This is the formula for determining compound interest.  I say growing wealth because I’ve already given my opinion on the most important formula in personal finance.

Below is the Compound Interest Definition:

$A=P(1+\frac{r}{n})^n^t$

• A= Amount
• P= Principal
• R= Interest Rate
• N= Compoundings Per Period
• T= Number of Periods

If you don’t want to do the math, you can just Google “compound interest calculator, 4” and there are many them where you can just plug in the figures.  Personally, I like to understand these things so I can see where my money is coming from, or in some cases, where it is going.

Since one of my goals is to reach financial independence, and I hope this site at least helps or inspires others to do the same, I figured it would be a good matter to discuss.

I wish this were taught in every school.  Or as well known by school-children as the formula for finding the area of a circle (because I do that all the time in real life).  I honestly believe lives would change, or take a completely different trajectory, just by understanding this formula.

The compound interest formula is why, back when I was dumb(er)- despite my monthly payments, the principals on my credit cards, student loans, never seemed to go down.

As I later learned, its why wealthy people tend to stay wealthy, or why the poor stay that way.  Its how the impoverished become wealthy.  Its how those remaining in the middle class will either ascend to wealth or fall to poverty.

#### Let’s break it down…

Consider this actual, real life scenario one of my buddies, Reginald* just went through.

Scenario:  You are almost 30.  You have a four digit retirement account.  You come into some money.  $20,000 dollars, to be exact. And it’s good timing, because your old car is shot. You need a vehicle. You can buy a really nice car for the entire 20k, or you could buy a nice enough car for 10k. Both are equally reliable, its just that the$20k is a super cool Kia, and the $10k is an Buick LeSabre the lady across the street only drove to Church and the grocery store (did anyone not have at least one grandparent who owned that car?). If you buy the Buick, you would just invest the remaining money in a tax-advantaged low cost mutual fund indexed to the S&P 500, and not think about it for the next 30 years. In this case, our good friend Reg here would have made his 2013 Roth IRA contribution prior to April 15, 2014. And then just made his 2014 contribution a little after that. As Reg said “the difference in the price of the cars is ten thousand dollars.” That is correct… and not how I would think of it. The real difference can be seen if we use THE MAGIC OF COMPOUNDING [at this point, I like to picture the curtain being drawn while Europe’s “Final Countdown” plays]. $A=P(1+\frac{r}{n})^n^t$ “A” in the formula represents the final amount, or the amount you end up with. We will leave that one blank for the moment. “P” represents the principal, or the money you have to invest. That would be$10,000.

“R” is the interest rate you expect to return on your principal.  Let’s use 9.71%, because that is the Compound Annual Growth Rate for the S&P 500 since 1988. It might be less than that.  It might be more.  I’m one of those mean reversion kind of guys.

“N” is the number of compoundings per period.  For the sake of ease, let’s just say your money compounds annually, or once a year.  So that number would be 1.

“T” is the number of periods.  If we aren’t going to touch the money for 30 years, then you guessed it.  In this example, T equals 30.

#### Plugging the numbers in, we have…

So, using the formula for compound interest, we can see that over 30 years, that Kia actually cost him about \$160,000 more than the Buick.  I don’t know about you, but I love this kind of thing.

In the words of the Gladiator, you know, from that movie, Gladiator, “Are you not entertained?”  But the focus of this post was on showing how seemingly small difference can have a HUGE impact on your financial future.  It’s all about the little decisions.  I’m always saying that mighty oaks from little acorns grow.  It’s good to understand how.