# Power of Compound Interest – A Case Study

Over at MarketWatch recently, was an interesting article entitled Make Your Kid Rich for \$1 a Day. I’ll let you go over there and read the particulars if you are interested. However, I think that the concept provides a great way to study the phenomenon of compound interest, and the elements that go into it.

### Compound Interest Only Works Over Long Periods

People love to quote Albert Einstein saying that the most powerful force in the universe is compound interest. What most people forget is, that as a physicist, Mr. Einstein was used to working on a very large scale, with a very long timeframe.

Let’s start at the beginning. Compound interest is not magical. It is merely the phenomenon of earning interest on your previously earned interest. So, if you invest \$10,000 and earn 10 percent interest annually, then you would earn \$1,000 in interest, and have \$11,000 at the end of the year. (Sort of, depending on how interest is paid and compounded, but let’s not quibble.)

The following year, you would also earn the same 10 percent interest. However, this time, you earn 10 percent on \$11,000, not just the original \$10,000. In other words, you are earning interest on the \$100 in interest you have already earned. That is the “compound” in compound interest, earning interest on the interest.

So, at the end of the second year, you earn \$1,100 interest (10 percent of 11,000). Your balance is therefore \$12,100. Next year you’ll earn interest on that amount.

## Case Study on Compound Interest

This is building up, and yes, over time, there will be a remarkable effect on the growth. However, notice what happened over the short-term period of a single year. The most powerful force in the universe added just \$100 of extra interest. Not exactly enough to supernova your finances.

In the third year, you’d earn \$1,210 of interest. That’s \$210 more than you earned the first year. Again, that’s good, but it’s not very powerful yet. Your total balance is still less than \$15,000.

### Compound Interest Over Time

This brings us back to our MarketWatch article where the author shows that you can make your kid rich for \$1 a day. Notice you can’t make yourself rich for \$1 a day.

Why not? There is not enough time. You’ll be dead before a dollar a day makes you rich. (Sorry.)

This particular article actually uses investing \$365 all at once at the beginning of each year. (I asked you not to quibble above, so I’ll pass on pointing out that it’s actually different than the headline.) Then, this money is invested in something that earns 12 percent per year. If you’re suspicious about that 12 percent, it is technically legit over the long term, but it is far from guaranteed.  But let’s not focus on that for now; let’s get to the power of compound interest!

Investing \$1 per day for 18 years and getting a really nice rate of return of 12 percent gives you, drum roll please…. \$20,348 when your kid turns 18.

Wait. What? Weren’t we making our kid RICH? That’s not enough to buy a new car these days, and certainly won’t be enough in 18 years. Maybe if we wait a little bit longer?

According to this article, even after 24 years, the kiddo will still only have \$35,857.

Where is this phenomenal power Albert Einstein was talking about?

You see, at \$1 per day, you won’t make your kid rich when they’re ready to head out into the world at 18 years old, or 21 years old, or even when they’re ready to start a family at 30 years old. You’ll make them rich when they are ready to retire.

A dollar per day invested for 18 years makes them rich when your kid is 66 years old. Not Paris Hilton rich, either your \$1 per day for 18 years plus compound interest gives your child \$4,185,342 when they retire. Awesome, but maybe not what you were hoping for.

## Compound Interest Rate

There is one more thing you should notice about the power of compound interest. The amount of interest really matters.

You recall above that the author used a 12 percent rate of return on the investment. You remember I told you to just go with it? Now let’s look at it.

Twelve percent is VERY HIGH to assume as a rate of return, even over a long period of time. For the author to sell it here, you must invest in small-cap value stocks for the entire time. You can’t get more conservative as you approach retirement, or anything of that nature. The more commonly used interest rate to sell this sort of thing is 10 percent, or maybe the historic rate of the S&P 500 index or Dow Jones Industrial Average, of around 11 percent.

Does just 2 percent matter? More than you might think.

The author did the same calculations for a 10 percent rate of return, and it turns out that your kiddo will only have \$1,455,159 at age 66. That’s kind of borderline in the “rich” department, and definitely not what you were thinking when you read the title. It’s also way less than the same investing at 12 percent, just 2 percentage points higher. And, if we’re really going to go down the reality path, keep in mind that \$1.4 million is going won’t be worth quite as much in 66 years, thanks to inflation.

### Compound Interest Takes a Lot of Time

The point of this personal finance article is not that it is a bad idea to invest money on behalf of your child. It certainly is not. In fact, I’d suggest you start saving more than a \$1 per day, and do it right away, not to make your child rich, but to send them to college. Open a 529 plan in put in a dollar a day, \$50 per month, \$1,000 per month, whatever you can afford. It won’t make your child rich, but it will let them graduate with fewer (or maybe no) student loans, and that’s probably a better gift than making them “rich” when they retire. Plus, you’ll be alive to see it.

### Compound Interest Case Study

The fact is, that compound interest really only works over a single lifetime if you continuously invest. Then, you earn compound interest, plus interest (and compound interest) on the continuing contributions. Having \$1 million when you retire doesn’t have to require your parents contributing \$1 per day when you are a child, it requires you saving \$5,000 or \$6,000 per year, and keep investing it for 35 years while earning 8 percent. Employer matches, increasing contributions, and so on, get you there much faster.

That is why all of those compound interest calculators or retirement planning calculators have a blank for ongoing investments. To have a baller retirement, you need to start saving now, you need to keep saving, and you need to keep investing and reinvesting. Anything else, and you can probably leave a nice little account for your kids.

The point is, that compound interest works, but if you want to see the results in your lifetime, you can’t let it do all the work.

Update: Forgot to link to the original article.