Compound Interest Math Formula – The Most Powerful Math in the Universe
Please see my earlier post, Part I – Why don’t they teach this math in school?
For the sake of blowing the lid off this vast cone of silence, here’s the compound interest formula:
Future Value = Present Value * (1+Yield)N
This is the formula you use if you want to see how money grows over time, to become “Future Value.” Present Value is the amount of money you start with. That could be $100, such as in my examples below, or likewise a series of $5,000 IRA investments each year. Present Value is whatever you’re starting amount of money is today.
Yield is the interest rate, or rate of return, you get per year. Usually expressed as something like 5.25% or 0.0525.[1]
N is the number of times you ‘compound’ the yield. In its simplest form as written above, if you compound annually, N is the number of years your money compounds.
Example of the power of compound interest: Early investment for retirement
When do you use this formula? You use it when you want to know how much your $100 invested today, or this year, will grow over time.
To offer you an extreme example, using the compound interest formula:
What if you invested $100 today, left it invested for the next 75 years, and you were able to achieve an 18% annual compound return? How big an investment does your $100 become?
The answer is $24,612,206.
Can I interest you in $24 million? Without working?
As I say that out loud, I feel like a late-night infomercial guy. And that feeling makes me want to take a shower. But the money and the pitch is nothing more than compound interest math.
I happen to believe there’s quite a few 20 year-olds who:
a) Could put their hands on $100 today for the purpose of investing in a retirement account, and
b) Would like, at the end their life, to boast a net worth of $24.6 million[2]
I know all you realists out there will say that 18% annual compound return for 75 years is a fairy tale, and of course I can’t disagree with you.
But I’m doing a magic trick here for the sake of making a point, so would you please suspend disbelief for just a moment and revel in the magic? The point is not to argue about what reasonable assumptions may be, rather the point is to show why knowing how to do compound interest math could be a life-changing piece of information.
At the very least, its a tool that every citizen should be armed with. Thank you.
To be slightly more realistic, but equally precise, with a series of other assumptions:
If you’re 20 years old now and you let your money grow for the next 50 years, at 12% yield, your $100 invested today becomes $28,900. That’s also an amazing result.
Try it and find the Future Value for yourself, by inputting into the formula
Future Value = Present value * (1+Yield)N
PV = $100
Yield = 12%
N = 50
Heck, having your money grow like this sure beats working for a living.
These facts are so amazing, I think, that they might induce a 20-year-old to forgo his XBox purchase this year, and invest the money instead in stocks, in a retirement account.
What about putting your money away in your IRA, $5,000 per year from age 40 to age 65, earning 6% return on your money every year? Would you like to know what kind of retirement you will have at age 65? Compound interest can tell you precisely the number.[3]
You’ll have $290,781.91[4]
And all of that becomes possible if we have some insight into the inexorable growth, the most powerful force in the universe, the one math formula to rule them all, compound interest.[5]
Please see Part I – Why don’t they teach this in school?
Part III – Compound interest and Consumer Debt
Part IV – Discounted cash flows – example of pension buyout
Part V – Discounted cash flows – using the example of annuities
Part VI – Conclusion and why everyone needs to know this math for the good of society
and Video Posts:
Video Post: Compound Interest Metaphor – The Rainbow Bridge
Video Post: Time Value of Money Explained
Addendum by Michael, added later: It turns out one of my high school math teachers not only does teach compound interest, but he included it in his math textbook, linked to here:
[1] I fear many of us learned how to convert a percent into a decimal in sixth grade, but not how to do anything useful with it.
[2] Yes, I hear you cynics, that this is in nominal dollars, and $24 million won’t buy them then what it buys today. But would you just stop being cynical for a moment, and appreciate the magic of compound interest? Thank you.
[3] If your assumptions are correct, of course.
[4] To achieve this calculation, you’ll have to add up 25 separate amounts, in a spreadsheet. The first amount, invested at age 40, compounds the most times and is expressed as $5,000 * (1+.06)25. The second amount, invested at age 41, compounds as follows: $5,000 * (1+.06)24. The third amount is $5,000 * (1+.06)23, all the way until the 25th amount, which is simply $5,000 * (1+.06).
[5] Thank goodness Sauron didn’t get his hands on the formula FV = PV*(1+Y)N, or else the hobbits would have been so screwed. Ancient legend has it in the Silmarillion that Sauron actually did acquire the compound interest formula, but he interpreted the mysterious algebraic symbols as high Elvish, a language he could not read at the time. Speaking of which, does anybody else want to use compound interest to become a Silmarillionaire? Um, not so funny? Ok, you’re right, but don’t worry, I’ll be here all night folks. Don’t forget to tip your waitress. And try the fish.
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6 Replies to “Part II – Compound Interest and Wealth”
Yes, but these types of safe yields don’t exist.
Its just examples to do the math for crying out loud.
It hurts my brain and it takes to long to set up an XL-sheet.
I always work with 72 –
I have $100 – how long does it take to double my money when I get 4 % compounded interest? and when I get 8 %, or 12%?
Easy
devide 72 by 4, 8 0r 12 and the time it takes in years = 18, 9 and 6 years!
Now what interest would I need to double my $100 in 4, 6 or 10 years?
Easy too: 72/4 or 6 or 10 = 18%, 12% or 7.2%….
Now apps needed – no calculators needed and if you can’t do it by heart, you should NOT put your $100 at risk!
I agree “The Rule of 72” is great BUT…there’s a lot more you can figure out flexibly, beyond the rule of 72, if you learn to use the formula and a spreadsheet…but I agree its a cool rule.
It is a Law of Economics that when supply is greater, price goes down. The fact that you can grow your dollars over time, is not good news, it simply means your dollars are getting more and more worthless. They are becoming more and more of them! It also means that more & more of your sweat & purchasing power is getting transferred over to the money manipulators, aka the Bankers. Therefore, Time is Not Money. Real money does not expand with time. Lets measure these investments in Gold, for instance, what then happens to the magic formula of compound interest? Useless! Gold (which is real money) does Not expand with Time! As banker, I am sure you know better.
As a ‘money manipulator,’ aka the Banker, I respectfully disagree.