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I remember when I was a kid, and I first heard about compounding. I had a passbook savings account with the standard rate of 5%. My mom and I were talking about how the savings would grow. I said, “so every year I am going to get $5 on my $100” “No,” she said, “Its going to be more than $5 because you are going to get interest on the interest”. I didn’t understand this for a long time and it all seemed very confusing, why couldn’t it just be $5 and make it easier.
Thankfully for all of us investors, that $5 ends up being a little bit more due to compound interest.
Simple interest is simple, but compound interest is God’s gift to investors and the Devil’s reward for debtors. It still amazes me how many people still don’t fully grasp the power of compound interest. If you are going to be a cheap person, you better get fully acquainted with it and make it your friend.
First, lets look at simple interest. You have a $100 and you earn a 5% interest rate, after a year, you have $105. After two you have $110. Pretty simple. Now if our compounding period is a year, after 1 year of compounding, you have $105. But after two years you have $105 plus $5.25 for a total of $110.25. OK, so its different but you might be saying, ‘What’s the big deal, its almost the same’ and for two years, you would be right.
Thankfully, we tend to live, invest, and unfortunately borrow for more than two years. Lets take our same example again but this time for 10 years. If we had simple interest, this is easy 5%*$100*10= $50 so we would have $150 in our account. For compound interest it’s a little harder to calculate. If we express our $105 relative to the original $100, its 105% or 1.05. Now we get to the real math part. If we compound that for 10 years it would be expressed as 1.05*1.05*1.05*1.05*1.05*1.05*1.05*1.05*1.05*1.05 = 1.629 or said another way, after 10 years of compounding we are going to have $162.90. Now you see how big the difference can be since we have nearly $13 more than if we just had simple interest.
If you want a quick way to calculate the effects of compounding learn to use the rule of 72. What that rule tells you is that if you're getting 10% interest, your money will double in 7.2 years. And if you're getting 7.2% interest you'll double your money in 10 years.
So, the math is relatively easy, just divide 72 by whatever interest rate you're getting and you'll get a good idea of how long it will take for your money to double. If you're getting 9% interest, your money will double in 8 years, but if you're getting 8%, it will take 9 years to double.
Now the rule of 72 works doesn't work for all interest rates. If you're getting 72% - it obviously will give you some false reading. But then again, you won't have to worry about being cheap if you're getting that rate of growth for more than a few years. For typical interest rates, in the 4% to 18% range, it works fairly well.
We used a passbook savings account example with 5% and a 10 year time horizon. Let’s look at something a little more interesting like your retirement. Instead of a $100 in a passbook savings account, my mom decides that at the ripe old age of 10, that she is going to put money into my retirement account that she doesn’t want me to touch until I am 75 years old. I have no clue what retirement is and I really would prefer just buying a bicycle but she is my mom, so I go along with it. Mom invests the $100 into the super low cost Vanguard S&P 500 Index fund and they waive the minimum for her since she offers to bake them some cookies (Vanguard just opened its doors a few years earlier so they are very welcoming). Can you guess what that $100 would grow into 65 years later if the average return of the fund is 10% over that time? Almost $49,000. That’s the magic of compounding. Compare that to investing in a “65 Year CD” at 5.00% where I would end up with about $2,300. Nice, but I am guessing I would go with the bike over the CD.
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