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compound-interestThe power of compounding interest

How money can grow quickLy

Albert Einstein is often quoted as saying “compound interest is the eighth wonder of the world.” The only problem is that he never actually said that. But whoever did was on to something, because compound interest is a fantastic way to turn a little money into a whole lot more.

So what is compound interest? Basically, it’s when the interest earned from an investment is put back into the investment, thus causing that interest to earn even more interest. This leads to fairly strong growth over time.

For the mathematically inclined, there is a formula to determine just how fast compounding interest can make your investment grow. That formula is:

Compound interest = [P (1 + i)n] – P

                            = P [(1 + i)n – 1]

In this formula, “P” is the principal (the initial investment amount); “I” is the annual interest rate in percentage terms (for our examples moving forward, we’ll put it at 10%); and “n” equals the number of compounding periods per year (could be one a year, or several).

Here are a few examples using this formula from the folks at Investopedia.com:

  • The compound interest on $10,000 compounded annually at 10% (i = 10%) for 10 years (n = 10) would be = $25,937.42 - $10,000 = $15,937.42
  • The amount of compound interest on $10,000 compounded semi-annually at 5% (i = 5%) for 10 years (n = 20) would be = $26,532.98 - $10,000 = $16,532.98
  • The amount of compound interest on $10,000 compounded monthly at 10% (i = 0.833%) for 10 years (n = 120) would be = $27,070.41 - $10,000 = $17,070.41

Let’s look at this another way, and so by asking a very simple question: If given a choice, would you choose one penny a day that is doubled everyday for 31 days, or one million dollars in cash?

Most people who are asked this question would take the million dollars outright. And why not? It’s right there and there is no waiting! But let’s take a look at the first option—the penny doubled every day for a month—to see what a combination of re-investing earnings and patience can do.

  • Day 1: $.01
  • Day 2: $.02
  • Day 3: $.04
  • Day 4: $.08
  • Day 5: $.16
  • Day 6: $.32
  • Day 7: $.64
  • Day 8: $1.28
  • Day 9: $2.56
  • Day 10: $5.12

So, after 10 days, you only have a bit more than $5. So far, it seems as though taking that million dollars is the better idea. But let’s keep on going …

  • Day 11: $10.24
  • Day 12: $20.48
  • Day 13: $40.96
  • Day 14: $81.92
  • Day 15: $163.84
  • Day 16: $327.68
  • Day 17: $655.36
  • Day 18: $1,310.72
  • Day 19: $2,621.44
  • Day 20: $5,242.88

Now we’re getting somewhere! The only issue is that it’s been nearly three weeks and we’re still not anywhere close to the million dollar mark. When amounts start to increase, however, the power of compounding really kicks in—and you can see that in the totals for the next eight days:

  • Day 21: $10,485.76
  • Day 22: $20,971.52
  • Day 23: $41,943.04
  • Day 24: $83,386.08
  • Day 25: $167,772.16
  • Day 26: $335,544.32
  • Day 27: $671,088.64
  • Day 28: $1,342,177.28

We finally reach one million dollars! But we’re not done yet:

  • Day 29: $2,684,354.56
  • Day 30: $5,368,709.12
  • Day 31: $10,737,418.24

Granted, you’re certainly not going to find an investment that doubles every day as the penny does in this example. What this example shows instead is the power of investing earnings on an investment back into that investment. It also shows that you don't need to be rich to invest and make money. You just need to be persistent about saving and have the patience to let it grow.  

So as you set your money aside—whether it’s in a simple savings account or retirement plan—remember to reinvest your interest and other payments back into it. Simply put, it’s one of the best ways to grow your long term savings.