Mathematical Formula for Compound Interest

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Compound Interest Math Formula – The Most Powerful Math in the Universe

Please see my previous post, Part I – Why don’t they teach this math in school?

To blow the lid off this vast cone of silence, here is the


compound interest

formula:

Future value = present value * (1 + return)NOT

This is the formula you use if you want to see how money grows over time, into “future value”. The present value is the amount of money you start with. This could be $100, as in my examples below, or even a series of $5,000 IRA investments each year. Present value is the amount of money you start 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 return. In its simplest form, as shown above, if you compound annually, N is the number of years your money is compounded.

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 give you an extreme example, using the compound interest formula:

What if you invested $100 today, left it invested for the next 75 years, and could achieve a compound annual return of 18%? How much of an investment is your $100?

The answer is $24,612,206.

Can I interest you in $24 million? Without working ?

Like I say out loud, I feel like some late-night infomercial guy. And this feeling makes me want to take a shower. But money and land are nothing more than compound interest calculations.

I think there are quite a few 20-year-olds who:

a) could get their hands on $100 today for the purpose of investing in a retirement account, and

b) Would like, at the end of their life, to boast of having


net value

$24.6 million[2]

I know all realists will say that a compound annual return of 18% for 75 years is a fairy tale, and of course I can’t disagree with you.

But I’m doing a magic trick here to make a point, so could you please suspend your disbelief just for a moment and revel in the magic? The point is not to discuss what reasonable assumptions might be, but rather to show why knowing how to do compound interest calculations could be life-changing information.

At the very least, it is a tool that every citizen should be armed with. Thanks.

To be a little more realistic, but just as precise, with a series of other hypotheses:

If you are 20 now and let your money grow for the next 50 years, at a 12% return, your $100 invested today becomes $28,900. It is also an incredible result.

Try it and find the future value for yourself, by entering the formula

Future value = present value * (1 + return)NOT

PV = $100

Yield = 12%

N=50

Heck, growing your money like that is better than working for a living.

These facts are so amazing, I think, that they might inspire 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 aside in your IRA, $5,000 a year from age 40 to 65, earning 6% back on your money each year? Would you like to know what type of retirement you will have at 65? Compound interest can tell you precisely the number.[3]

You will have $280,781.91[4]

And all of this becomes possible if we get a glimpse of inexorable growth, the most powerful force in the universe, the one mathematical formula to rule them all, compound interest.[5]



[1] I’m afraid many of us have learned how to convert a percentage to a decimal in sixths, but not how to do anything useful with it.

[2] Yeah, I hear you cynical, that’s in nominal dollars, and $24 million won’t buy them then what they’re buying today. But would you stop being cynical for a moment and enjoy the magic of compound interest? Thanks.

[3] If your assumptions are correct, of course.

[4] To perform this calculation, you will need to add up 25 separate amounts in a spreadsheet. The first amount, invested at 40 years, is compounded the most times and is expressed as $5,000 * (1+0.06)25. The second amount, invested at age 41, is composed as follows: $5,000 * (1+0.06)24. The third amount is $5,000 * (1+0.06)23until 25e amount, which is simply $5,000 * (1 + 0.06).

[5] Thank God Sauron didn’t get his hands on the formula FV = PV*(1+Y)NOT, otherwise the hobbits would have been so fucked up. Ancient legend has it in the Silmarillion that Sauron did indeed 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 anyone else want to use compound interest to become a Silmarillionaire? Uh, not so funny? Ok, you’re right, but don’t worry, I’ll be here all night. Don’t forget to tip your waitress. And try the fish.

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