Bill Totten's Weblog

Saturday, September 26, 2009

Magic of Compound Interest

by Theodore Hansson

The Rule of 72

Have you always wanted to be able to do compound interest problems in your head? Well, let's be honest - probably not.

However, it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential mortgage note (or any investment) is likely to be. And it's surprisingly easy to do in your head ... once you know how.

The rule says, that to find the number of years required to double your money at a given interest rate, you simply divide the interest rate into 72. That's why it's called the "Rule of 72"!

For example, if you want to know how long it will take to double your money at eight percent interest, you would simply divide eight into 72 and you'll get nine years. This is assuming the interest is compounded annually.

As you can see, the "rule" is remarkably accurate, as long as the interest rate is less than about twenty percent. At higher interest rates the error starts to become significant.

Of course, you can also run it backwards. For example if you want to double your money in six years, just divide six into 72 to find that it will require an interest rate of about twelve percent.

Quite easy! You don't need to be a "math-whiz" to do it. Now, let's continue this fascination subject with some fun exercises.

Famous Compounding History

The history of compounding computation goes back thousands of years, at least to the Babylonians.

However, the most famous compounding exercise of the all has to be the sale of the Island of Manhattan in New York in 1626.

It was May 24 1626 when Peter Minuit, a director of the Dutch West India Trading Company, bartered sixty guilders (about $24) worth of beads and trinkets to local Lenape Indians in exchange for the island of Manhattan. There is some doubt that actual beads were involved in the transaction, but that's another story.

It's too bad, but no deed or official document of the island's sale to the Dutch from the Lenape Indians exists today.

Now, an interesting investment question arises ...

Was this a good deal for Minuit or not?

Let's look at the deal. What would be the value of $24 if Minuit had invested it instead at eight percent interest, compounded annually for 374 years? (1626 to 2000)?

At first sight, this seems like the deal of the century. Given today's real estate values in New York, this appears to be a great deal for Minuit. But not so fast ... remember, you always have to do the numbers!

Also, keep in mind that Minuit bought undeveloped land ... not buildable lots with sewer, water, streets et cetera.

Now, if you run the numbers, you'll discover that the original $24 would have grown to a staggering ...

$76 Trillion!

Yes, you read it right, not million, not billion, but trillion.

This is actually more that the estimated value in today's dollars of all the real estate on this 31 square mile island.

So which would have been the better investment?

The Magic of Compound Interest

Let's continue for some more fun. Imagine that back in 1930 your grandparents scrimped and saved and placed $100 in a trust fund where the money would accumulate for their grandchild (you).

And imagine that the $100 remained in this fund for some seventy years, until the year 2000, earning the average rate of twelve percent. How much money would you think you would have today from that initial $100 investment?

The answer, incredible as it may sound, is ...


Remember, we're only talking about a single $100 investment, not $100 added per month or per year!

Of course it might have been hard to get twelve percent year-after-year, some years would have been a lot less. But then again, remember the early 1980s, when it was not uncommon to get fifteen to eighteen percent interest on your money.

Just imagine if your grandparents and your parents had also added just small amounts of money every year to your fund, how much money you would now have!

If you're interested in playing around with compound interest, there's a nifty compound interest calculator at:

Here's How Compounding Works

Compound interest pays interest not only on the principal, but on the interest as well, increasing the rate at which your money grows.

For example if the interest was compounded yearly and you started with a $100 investment at a ten percent interest rate, you'd have earned $10 interest the first year, and would now have $110 at the end of the first year.

In the second year, you would earn interest on $110, giving you $11 in interest in the second year, so at the end of the second year you would now have $121, and so on. So after twenty years you'd end up with $672.75!

Add Payments for Even Greater Growth

Now, if you'd added additional money to your savings every year your money would of course grow even faster.

For example, if you save $2,000 a year at ten percent interest, you'll have more than $35,000 after ten years.

Not bad, but ... if you keep at it another ten years, (double the initial period) you'll have far more than $70,000, (double the $35,000).

In fact you'll have $126,000!

Go for another ten years and you'll accumulate about $362,000. Another ten - that would be forty years or a typical "working'' lifetime - and you'll be ... are you ready for this ...

Almost a Millionaire - with $973,703.62!

Generally, any series of regular or steady payments is called an annuity .

You can play around with annuities at:

Now, you might wonder what does all this have to do with mortgage notes?

Well, you have to wait until next time, when I'll show you how you can actually lower the interest rate on a note or a loan and still come out ahead ...

Way Ahead!

Remember ...

"You Don't Have To Get It Perfect ...

You Just Have To Get It going!"


Article by Theodore Hansson of Theodore Hansson Company. Theodore has helped thousands of ordinary people succeed in their own home-based business, brokering loans. Visit him at for free "how-to" information as well as a free subscription to his newsletter "Loan Brokering Tips & Tricks".

Bill Totten