Compound Interest Explained
Compound interest is the magical phenomenon that grows your money exponentially. It can be more powerful than a passive income stream or even your paycheck. It's probably the greatest path to wealth building that has ever existed.
Let's get you up to speed on compound interest so you can clear the way to becoming rich. We're going to talk about compound interest, what it is, how to use it, and most importantly, how to get really rich using compound interest. Now, I'm not going to get too technical with compound interest and go through the formulas, but we are going to go through some examples to have a better understanding of what compound interest is and how to get really rich using it.
And at the end, I'm also going to show you a calculator that I use on my phone almost every day that uses compound interest to help quickly calculate the numbers for you.
Okay. So I'm going to go jump right into it and we're going to go through a simple interest calculation so you can understand how compounding works. So this is really the building blocks of it all. So let's go ahead and start with our $100. If we invested $100 at an 8% rate of return, we'd simply take this $100 and multiply it by 8%.
Which is 0.08, and that would equal $108. So if we invested $100 at 8%, simple interest would give us $8. Now, what most people think is, that would occur each and every single year. So over a 30 year investment horizon, if we invested $100 and got $8 or 8% every single year, we would simply simple interest simply multiply our $8 by 30 years.
So we would take our $108 we could take our $8 gain, multiply it by our 30 year time horizon. And that would give us $240. Now we started with $100, so we would simply add the two together. 100 plus are $240 would give us $340 So with that example investing $1, we would have to wait 30 years for that $1 to turn into $3.40.
But with compound interest, we're actually taking that extra $8 every single year and making it work for us. So here's how that works. If we go back to the same example, what we're doing is we're not only investing this $100 that we started with, but each and every single year we're taking this $8 and making it work for us.
So while after the first year, we only have $8 in year two and beyond, we're taking that $8 and then also applying that interest rate. So here's what that looks like. So taking that same example of $100 and multiplying it by our 8%, we are making $8. So I'm only putting the gain over here now in year two.
We're going to take our $108 and multiply that by 0.0, eight or 8%. So we're having this $8 now work for us. So if we just simply take this $8 and multiply it by 0.08, so if we take it out by $8 times 0.08, that's going to be an additional $0.64. So in year two, we're going to have $8 and 60 for more sense than we did from the previous year.
So what that's going to look like an additional $8. We're just going to multiply that $8 by our 8%, which is 0.64. That means in year two, we're now going to have $116.64. So we didn't just make an additional $8, we made an additional $8.64. So in years three, we're now taking that additional $16.64, and then multiplying that by the 8%, you have to think of it like a snowball.
It starts small. But over time, it's significantly increases in size. The further along that we get. So to understand how this works year after year, over a longer time frame of 30 or 40 years, I want to go to a Google sheet so we can see all the math really quickly. To see the effects of what is exactly going on with compound interest.
So let's take our same example on this Google sheet of $100 And that's what we're going to start with. And let me go ahead and increase this so we could see this a little bit better. And this is going to be in dollars and cents will increase the font here. And our $100 is what we're going to invest, and it's going to be at an 8% rate of return.
So I'll change that to a percent of 8%. And then we will start our year one through 30. So this is going to be one to going on down. We're going to change this to a number And we're going to put that to number right there, going down to 34. Highlight that pull it down for 30 years. We'll actually go to 40 just so we can see the total effect here.
And we're going to take this column right here and I'm going to take away those zeros. There we go. And this is going to be our initial investment of $100 so we can quickly change it so I can show you all the effects. And this is going to be multiplied. So this multiplied by our 8%, which will give us our $8.
And then this is going to be the sum of the $100 plus how much we're going to make. And that's one. 08. So then our year two will then show what we made after year one, which is our 108. So we're going to say equals this number right here. And then we can see this. So I'm going to go ahead and make this the same number each time.
So the purple will be the same 8% each and every single time. So we can go ahead and drag this down, drag this down and drag this down. And should start to populate here. So you could see all the numbers here. Drag it all the way down to our 40 years. I'll expand these so we could see them a little clearer and we'll scroll a top and then we'll start talking our way through this.
So in year one, we invested our $100 and we made $8. So that totals $108. Now, in year two, we're starting with our one and. So we're making that other $8 starting to work for us. So then that's where we get our additional $0.64 because now we have that $8 also working for us. So rather than just making the $8 each and every single year, we're making a little bit more like that snowball that we talked about.
So we can put it right here that we're this is the gain for each year. This is the ending balance for each year. And we can expand that. So instead of seeing and I'll just organize this a little bit better so we can see it center this there now rather than just having that $340 that we talked about with the simple entries.
So we started with $100 at simple interest means the 8% was only giving us $8 every single year, but we weren't re-invest getting that $8 that we were actually making. And that is what compounding does for us. So our initial investment of $100 over 40 years would turn into $2,172.45 or set another way if we go back to our sheet and we change this to $1.
$1 invested over 40 years at an 8% compound rate of return would give us $21.72. So first we had a simple interest. $1 at 8% would only give us $3.40. But because we're using compound interest, our $1 now becomes $21.72. Now here's what's really interesting about looking at compound interest. And if we go back to this example and we put in our $100 again, it is how fast it grows.
The longer that we actually wait. So in the early days we're looking at $108, turning to one $116.64 But as we go further down to go from year 39 to year 40, we're making significantly more money per year. We're going from $149. Then in the 40th year we made $160.92. So it is really that snowball and that growth.
So when we're looking at reaching our goals, it's not just about the annual rate of return, but it's also about the time frame that we're investing What it really means is that the earlier that you start investing, the better off you're going to be when you hit retirement. And we can also see from here that even though we started with $100, we ended with 21 72, 45 significantly more.
So it doesn't necessarily mean that you need to start with a lot of money in order to be rich. You could start with a little sum of money. Start that investment process and then wait over time for it to grow So to put this into perspective, that $5 cup of coffee that you're spending today is really $100 away from your financial future.
Now, I'm not telling you that you shouldn't go out and buy cups of coffee or spend the money any way you see fit, because you certainly can. But hopefully this concept puts a higher value on each dollar that you're spending today. So now let's go ahead and jump into that calculator I was talking about in the very beginning.
So you can quickly do this math and really understand the concept of compound interest. So this is the calculator that I use on my phone, and I'll leave a link in the description at the bottom. I don't have any affiliation with the calculator I think it cost a couple of dollars. I'm sure there's free versions out there, but I just want to go through so you can see exactly how this works.
Now I'm going to go through the same example we just went through, and I'm going to go through this rather quickly. Just you can get an understanding of how a calculator works and you can do this math really quickly to understand compound interest. So I'm going to start with one year and I'm going to hit one the shift key and the end to give us the one year 8% rate of return, same thing.
And then our $100 and we're not going to put anything for a payment that's systematic payments and for future value. So you can see our $108 and just ignore the negative symbol or the negative sign. And if we jump this one to 40 or 40 years and hit shift and end and go ahead and hit the heavy, we can see that we get two that are $2,172.45.
Now normally if you're looking at this and you've already are familiar with the calculator, you would say, well, wait a second shift, you do 12 payments a year or even 365 payments a year for compounding on a calculator. Yes, but I'm simplifying this walkthrough. Just, you can understand the concepts. So go ahead and check out some of my other videos to go through the calculator math, and I'll do some future videos.
And of course, if you have questions, let me know in the comments down below on the calculator use for compound interest. So if we do all of this, we can even take it a step further and start to add in payments. So let's say that you started with $100, but you wanted to contribute additional money. Moving forward, let's say $100 on a monthly basis, we would change our payments per year, which is right now at one.
We're going to change it to 12 payments per year. And you can see it says 12 now up there. We're going to go ahead and reenter in our 40 years because we're going to have 480 months and an 8% with our initial investment of $100. But we're going to contribute $100 on a monthly basis. And then we can quickly figure out what that would look like at an 8% rate of return.
And then we're going to get 353,855. So that was all basically a simplified walkthrough of how compound interest works. And also what would it look like if you started adding money towards your investments on a monthly basis? But you might still be wondering where I got the 8% from. And it really is more of a conservative number or a projection.
It's an estimate. We don't really know what your investments will do over the long haul. We only see what history has shown us and apply it towards the future. Of course, that's not a guarantee but to show you those numbers of the S&P 500 over longer time frames, we can go to this chart right here. And this is the S&P 500 going from 2018 back to 1926.
And I don't have the updated numbers for 2021 but from 2018 to 1926. The S&P 500 did a compound rate of return of 10%. And even if you go back many years from 20, 18, 30 years back, if you're looking at 1988 we can see it did 10.2%. And if you look at any of these numbers going back further, you really don't see anything that even goes below 9%.
I don't think any of these go below 9% going through it. Now none of them, but if you go to the earlier years, you can see that it's a little more volatile or those numbers change a little bit more. Sometimes they're lower than are 8% target, but over longer time frames, you can expect a little bit higher rate of return.
Again, history isn't a guarantee of future performance. But that is where we're pulling the numbers from. Now, you can certainly go in and put in 10%, but that really doesn't do anything to the actual investment. It's just a projection to give you an idea of how much you need to start with today or how much you have today.
What would happen if you start adding to that on a monthly basis or a systematic one? And what would it look like over that long haul? So hopefully this give you a better idea of how compound interest works and a calculator. You can actually run some math very quickly right from your phone.