Basics: Compounded Interest

Let’s take a look at compounded interest to find some motivation for investing. This is a simple concept that can be confusing at times. I believe Einstein was quoted saying, “The most powerful force in the universe is compound interest.” The idea behind compounded interest is that growth is proportional to the current amount.

If the annual interest rate for a savings account is 5%, how much you expect to get back if you put in $100 and wait 3 years.

The naive first guess would be $115 since you get 5% each year. $100(original) + 3*0.05*$100 (interest) = $115.

The real answer is $115.76 dollars. You get this by accounting for the interest on the interest gained each year.

End of Year 1: $105 = $100*(1.05)
End of Year 2: $110.25 = $100*(1.05)*(1.05)
End of Year 3: $115.76 = $100*(1.05)*(1.05)*(1.05)

That doesn’t seem like that big of a difference, but let’s look at what happens when the interest rate is 25% instead of 5%.

$100*(1.25)*(1.25)*(1.25) = $195.31

You would nearly double your money if you can maintain a 25% growth each year for 3 years. That’s quite different from the $175 one would think. When you invest your money, it grows and you can invest that money also, so it can grow even faster, then you reinvest that money and it grows even more. You reinvest your gains to get compounded growth. By choosing investments, one wishes to maximize the growth, because small amounts can make a big difference over the long term.

Now let’s look at what the difference would be in a decade if we invested $100 in a variety of investments.

CD (5%) – $ 162.89
Index Fund (10%) – $ 259.37
Good Stock Pick (15%) – $404.56
Warren Buffet (25%) – $931.32

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