Answering Riddles: Compound Interest

So, did you do the math? What did you find out?

If you missed it, go back and have a look at Saturday's riddle.

Okay, let's add it up for you:

Day - Plan A - Plan B
1) $100.00 $0.01
2) $100.00 $0.02
3) $100.00 $0.04
4) $100.00 $0.08 (Plan B people aren't even making a dime. This riddle doesn't even seem fair.)
5) $100.00 $0.16
6) $100.00 $0.32
7) $100.00 $0.64 (It's been a week, and the Plan B people haven't even made a dollar a day yet! What were those Plan B people thinking?)
8) $100.00 $1.28
9) $100.00 $2.56
10) $100.00 $5.12
11) $100.00 $10.24
12) $100.00 $20.48
13) $100.00 $40.96
14) $100.00 $81.92 (Two weeks down, and the plan B people still aren't making as much as the Plan A people! Halfway over, and the plan A folks are clear winners. Anybody want to switch sides?)
15) $100.00 $163.84
16) $100.00 $327.68
17) $100.00 $655.36
18) $100.00 $1,310.72 (Hey, wait! These plan B numbers are getting big!)
19) $100.00 $2,621.44 (Wait! The plan B people just got more in one day than the plan A people have made total, so far!)
20) $100.00 $5,242.88
21) $100.00 $10,485.76 (Three weeks down, and the plan B people are now making 100 times what the plan A people are getting! Things weren't like this a week ago.)
22) $100.00 $20,971.52
23) $100.00 $41,943.04
24) $100.00 $83,886.08
25) $100.00 $167,772.16
26) $100.00 $335,544.32 (That's over a third of a million dollars in one day!)
27) $100.00 $671,088.64
28) $100.00 $1,342,177.28 (Over a million dollars? Are you serious?)
29) $100.00 $2,684,354.56
30) $100.00 $5,368,709.12 (Five million dollars? What's happening here?)

The total payout? Under plan A, you'd get exactly $3,000. Under plan B, you'd end up with $10,737,418.23. It would take more than 3,000 months of making $3,000 a month to get that much!

So what happened here? How did we get from a penny to five million dollars?

The answer is a little principal called "Compound Interest." Albert Einstein is reported to have said, "Compounding interest is the greatest mathematical discovery of all time." I don't know if he said it or not, but as you can see in the above example, it's power can't be understated.

What compound interest means is this: If you have some money, and you put it in a place that earns interest, not only will your money earn interest, but the interest you earned will also earn interest. Before too long, you get to see interest earning interest on interest earning interest. This "stacking" of interest in on interest is called "compounding."

The money you make makes you more and more money the longer you let the interest "compound."

This is what it means if you hear that money is "compounded annually" or "compounded monthly." It describes how often they add the interest on top of the interest. If it's compounded annually, the interest only stacks up once a year. If it's compounded monthly, the interest stacks up every month. And if it compounds daily, then every single day, you're earning interest on the interest from the day before.

As you can see in the above example, the main thing you need in order to harness the power of this principle is time. The more time you have, the greater the principal can work for you. After one or two weeks, it didn't seem like we were doing that well. But the longer the time went on, the more dramatic the results became. If you extended this out further, you can imagine how quickly it would build.

The other important element is the interest rate. What percent interest you're making on your money can greatly accelerate the growth of your money. My example was extreme--we doubled our money every day. But you can double your money at any interest rate. To figure out how quickly, we use the Rule of 72.

To use the rule of 72, just divide the annual interest rate you're getting into 72. That's how many years it would take to double your money. At 10% interest, your money will double in 7.2 years. At 12% interest, your money would double in 6 years. On average, Coca Cola stock has returned 16% interest. At that rate, your money would double in less than 5 years.

How quickly does that add up? Well, let's say a teenager puts $2,000 away on his 16th and 17th birthdays. If he got 12% interest on that, he'd retire at 65 with $1,094,079.72, even if he never contributed another dime towards retirement.

On the other hand, if I, the guy turning 30 this year, put $2,000 a year in the same fund from now until I retire--that's $72,000, total--I'd still end up almost $10,000 shy of matching him. I'd still end up a millionaire, but with a $68,000 higher pricetag.

But even then, it still cost me less than $75,000 to become a millionaire. Those are still great numbers.

So now that you know how interest works, think about how your credit card companies are working with you. If they're getting 20% interest on their money, what's 72/20? Like, three and a half? By giving money to you at that interest rate, they can collect double their money from you in just three and a half years. You think you're paying it down, but you're really not.

If you only pay the minimum, the average credit card bill takes 48 years to pay off. The credit card company wants you to keep their money. They're more interested in letting that money compound, and letting you pay that.

Remember the other famous saying about compound interest: "Thems that understand it, earns it, thems that don't, pays it."