Explaining Compound Interest

7 years. That’s how long it takes to double your money if you can invest it and receive 10% interest.

Interesting, isn’t it? – One of those small truisms that forces you to ask questions. “How’s that possible?” What if I got more than 10% interest? What if I got less? Then how long would it take to double the money?

Questions turn to possibilities. Soon the fog begins to lift.

“OK – OK,” you say to yourself. “IF it takes 7 years for my money to double at 10%, then what happens to it in 14 years? It triples, right?” Wrong. It QUADRUPLES. That is, every $1 you invested would turn into $4. To put that a bit more into real-life perspective, $10,000 becomes $40,000. Or, if you like to think big… $250,000 becomes a cool $1 MILLION DOLLARS.

Here’s one for you. Let’s pretend you were that lucky person who invested the $250,000 that became $1,000,000 just 14 years later. How long would it take for that $1,000,000 to turn into $2,000,000? That’s right. Just another 7 years IF you could continue to get a 10% return on your investment.

Enough dreaming. Let’s explore and see how all this is possible.

First, a rule. Actually, the only rule. Remember this one and you’ll understand compound interest. It’s called the RULE OF 72.

Mathematically, the Rule of 72 looks like this: 72 / i = y. In this formula i equals yearly interest rate and y equals number of years for money to double.

If we put the Rule of 72 into words, it would read like this: Divide 72 by the rate of interest to calculate the number of years that it takes money to double.

Now let’s look at a simple example.

Assume you have $100 to invest. You go to the bank and open a savings account paying 2% interest. You wonder how long it would take for that $100 to double if you never made another deposit. Let’s see if we can figure it out.

The Rule of 72 says that we should divide 72 by the rate of interest, which in our case is 2%, to calculate how many years it will take to double. OK. Let’s do it now: 72 / 2 = 36.

So, if we open our bank account with $100 and the bank pays us 2% interest per year, it will take 36 years for that sum to double to $200 if we do not make any additional deposits or withdrawals.

At 5%, it would be: 72 / 5 = 14.4 years and, as we saw at the beginning of this article, at 10% it would be 72 / 10 = 7.2 years which, for the sake of simplicity, I rounded down to 7.

Are you with me so far? I hope so. Because now we’re going to take it a little bit further and, to see how the Rule of 72 works, we’re going to see what happens each year.

Let’s take our example of investing money at 10% interest.

Start of Year 1: We invest $100
At the end of Year 1, the bank pays us the interest that was promised. We calculate the interest by multiplying the amount of our deposit by the interest rate. So $100 x 10% interest= $10 interest. Running total at the end of year 1: $100 + $10 = $110.

Now it gets interesting.

At the end of year 2, what does the bank pay us assuming we’ve not made any additional deposits or withdrawals? Another $10, right? Wrong. This time they’ll pay us $11 interest because they are now paying interest on our $110, not just the $100 that we initially deposited. Our interest is compounding. Some like to call it magic, but it’s not. It’s actually very simple and, if you think about it, makes perfect sense. After all, the interest that we earn is our money and we’re letting the bank keep it in the account. So of course they have to pay us interest on the new amount.

Let’s lay out year-by-year example of what happens, this time without explanations. Just watch the numbers grow.

Year 1:
$100 x 10% = $10 interest. Running Total: $100 + $10 = $110

Year 2:
$110 x 10% = $11 interest. Running Total: $110 + $11 = $121

Year 3:
$121 x 10% = $12.10 interest. Running total: $121 + $12.10 = $133.10

Year 4:
$133.10 x 10% = $13.31 interest. Running total: $133.10 + $13.31 = $146.41

Year 5:
$146.41 x 10% = $14.64 interest. Running total: $146.41 + $14.64 = $161.05

Year 6:
$161.05 x 10% = $16.11 interest. Running total: $161.05 + $16.11 = $177.16

Year 7:
$177.16 x 10% = $17.72 interest. Running total: $177.16 + $17.72 = $194.88

Year 8:
$194.88 x 10% = $19.49 interest. Running total: $194.88 + $19.49 = $214.47

Let’s stop. We see here that it takes somewhere between 7 and 8 years for money to double at 10% interest. The same type of year by year analysis can be performed for any amount of starting money at any desired interest rate.

There are many variations on this concept and lots of things that can happen to money in between the starting time and the time it is withdrawn. Additional deposits. Perhaps some withdrawals. All are going to play a part in affecting the ultimate outcome. Perhaps, now that you know and understand the RULE OF 72, you will see that it’s never to late to start saving for the sake of your future and that of the ones you love.

I’ll leave you with this opportunity to ponder. The next time a baby is born, instead of a trinket that will soon be forgotten, if you were to give, as a gift, a few shares of a good mutual fund that earned an average of 10% a year, how much will those shares be worth by the time the baby is ready to get married, or go to college? How much would they be worth if the baby never withdrew the money, but instead just let those shares grow until retirement age? The answers will shock you.