2 – Compounding

Compounding

“Compound interest is the eight wonder of the world.  He who understands it, earns it… he who doesn’t… pays it.”  ~ Albert Einstein.

Compounding is what happens when you reinvest the interest income you earn from loaning your money.  Compound interest is the interest that is earned on reinvested interest income.  Take our previous example (in 1 – Time Value of Money and Interest Rates) of U.S. Treasury Bonds paying 1.75% interest per year.  We initially invest $100 (at the beginning of year 1), and at the end of year 1 we earn $1.75.  If we choose to reinvest that $1.75, instead of spend it, that $1.75 will be added to our original capital base of $100, and it will help us generate even more interest over year 2.

Original Capital Base (beginning of year 1) = $100

Interest Payment (received at the end of year 1, and reinvested) = $1.75

New Capital Base (end of year 1, beginning of year 2) = $101.75

So how much interest will we receive at the end of year two?  We’ll earn $1.78.  ($101.75 x 1.75%).

If we add that $1.78 to our capital base, how much will we earn at the end of year 3? $1.81.

You can see how this amount adds up.  After three years, we’re earning more than our original $1.75, simply because we chose to reinvest the proceeds!

I realize this example seems ridiculous.  What can a person do with three extra pennies at the end of one year, and six extra pennies at the end of the next?  So, let’s up the ante and use a more dramatic example.

At the time of this writing, you can purchase preferred stock of Wells Fargo Bank for about $28 per share.  Don’t worry about what preferred stock is, just know that it’s similar to a bond, only this bond yields 7% per year!

Note: the income we get from stock we call dividends, while the income we get from bonds is called interest.  

7% of $28 is about $2.00.  This is what we’ll get paid at the end of year 1 by investing our $28 in Wells Fargo’s preferred stock.  If we reinvest our $2.00 at the end of the first year, our capital base will grow to $30 ($28 + $2 = $30).  Since our investment in Wells Fargo’s preferred stock still yields 7% per year, our new capital base of $30 will pay us $2.10 at the end of year two.  Add this $2.10 to our capital base for year three, and our income at the end of year three will be $2.25.  If this continues, our initial investment will double in ten-years!  Simply by setting aside $28 and letting it earn 7% interest (or in this case, dividends), and letting that interest compound, we can double our money in ten years!

The Rule of 72.  You can find roughly out how long it will take your money to double when compounding by dividing your interest rate into 72.  E.g. at 7% interest, your money will take (72 / 7) 10.3-years to double.  At 9% interest, your money will take (72 / 9) 8-years to double.

Compounding, simply put, is the exponential growth of money due to the reinvestment of interest and/or dividends.  Compound interest is the interest that you earn on reinvested interest payments.  It is a powerful concept – available to all but only used by few.