How Compound Interest Works

You may have heard of compound interest before, or compounding.  But how does it work?  Well, this is your lucky day!  I’ll show you how it works.

It’s easiest to imagine interest in terms of bank products, like savings accounts and CDs, because lots of people are familiar with them.  So, let’s imagine that you open a savings account at a bank.  Here’s the deal:  you put in $100 and they will pay you 5% interest at the end of the year. Here’s what the first year looks like:

Compound Interest, Fig. 1
Year Beginning Balance Rate Interest Earned Ending Balance
First Year $100 5% $5 $105

You put in $100 and made $5 – clever you!  At the end of the first year you have $105 in your account.  Now, you could take out the $5 and spend it, or you could leave the $5 in the account.  Let’s say you choose to leave the $5 in the account to start compounding, what would the second year look like?

Compound Interest, Fig. 2
Year Beginning Balance Rate Interest Earned Ending Balance
First Year $100 5% $5 $105
Second Year $105 5% $5.25 $110.25

There.  Now we’re starting to make some progress.  Notice, you got more interest in the second year than in the first.  This is because the beginning balance in the second year is larger than the beginning balance in the first year.  that’s what happens when you compound your interest.  Let’s see where you are in five years.

Compound Interest, Fig. 3
Year Beginning Balance Rate Interest Earned Ending Balance
First Year $100 5% $5 $105
Second Year $105 5% $5.25 $110.25
Third Year $110.25 5% $5.51 $115.76
Fourth Year $115.76 5% $5.79 $121.55
Fifth Year $121.55 5% $6.08 $127.63

As you can see, your interest earned increases each year, as does the ending balance.  Remember – this is money you didn’t have to work for!  Let’s see what happens in the 50th year.

Compound Interest, Fig. 4
Year Beginning Balance Rate Interest Earned Ending Balance
Fiftieth Year $1,092.13 5% $54.61 $1,146.74

I am not kidding.  If you put $100 in an account for fifty years at 5%, compounding annually, you will end with $1,146.74.  What if you would’ve put in $1,000?  You’d have $11,467.40.  Here’s an illustration the compound interest curve for $100 at 5%.

Illustration of Compound Interest Curve
As time passes, the curve will become steeper.  This is why you always hear people saying that it’s important to save when you’re young.  Compound interest is most substantial at the end of the curve.  If you start earlier, then you’ll have a longer compounding period.

So, now that you know how compound interest works, you plan to start a compounding project of your own, right?  Right?

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One Response to How Compound Interest Works

  1. essay says:

    That was an excellently written essay, thank you so much.

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