Understanding the Magic of Compounding

Money works hard for you when directed properly. On some level, most people acknowledge this, but still underestimate how much money they can make simply by investing. 

To understand the magnitude of investing, we first have to understand the magic of compounding.

Interest on Interest

 Let’s say you have a $1,000 bond that pays you 5% a year. If you buy it this year and sell it next year, you’ll end up with $1,050, which is your original investment plus the 5% interest payment. If you held it for longer, you would receive 5% for every year that you held it, then get your $1,000 back at the end.

Now, instead of holding it for 1 year, let’s say you hold it for 5. At the end of the 5th year you would have $1,276.3

Wait… if you’re getting 5% every year, shouldn’t you have $1,250? Instinctively, you would expect your returns to look something like this:

 

Year 0

$1,000

Year 1

$1,050

Year 2

$1,100

Year 3

$1,150

Year 4

$1,200

Year 5

$1,250

 

So where did this extra $26.3 come from? The answer is that you earned interest on interest. Instead of earning 5% on $1,000 every year, you’re actually earning 5% on the previous balance. So from year 1 to year 2 you don’t earn $1,000 X 5%, you’re actually earning $1050 X 5%! Your returns really look like this:

 

Year 0

$1,000

Year 1

$1,050

Year 2

$1,102.5

Year 3

$1,157.6

Year 4

$1,215.5

Year 5

$1,276.3

 

Compounding just means that instead of increasing linearly, an asset increases in value exponentially. This is where the magic happens. But who cares about an extra $26 over 5 years? To show the real power of compounding, you have to look at it over a longer time period. 

For this example, let’s say you want to retire in 30 years. You buy the same bond we mentioned, but now you’re holding it for 30 years instead of 5. At retirement you would have $4,322. That’s more than 4 times your original investment, and without compounding you would only have $2,500. 

Investing doubled your money, then compounding doubled it again.

The Rule of 72

This is an easy rule of thumb to estimate how long it takes to double your money. To figure it out, take 72 and divide it by the interest rate (or return) you expect to receive. In the case of our 5% bond, 72/5 is 14.4, meaning it takes 14.4 years for your money to double. 

Does this agree with the number we got earlier? Well in 30 years your investment should double twice, so it would be about $2,000 in 14.4 years and $4,000 in 28.8 years. So by the 30th year, it makes sense that you would have earned a bit more than 4 grand. Using this tool, we can explore how much an investor could earn by investing in higher return assets like stocks.

The average return of the S&P 500 for the past 60 years is 11% per year, more than double the yield on our bond from earlier. Let’s assume we’ll get the same return going forward. Using the rule of 72, we estimate that our money will double every 6.5 years (72/11). Using the same $1,000 over 30 years, we would expect to have a whopping $25,760 at retirement!

By doubling our return, we increased our total gain by 6 times.  

 

 

 

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