## This Is How Compound Interest Actually Works

### Craig Donofrio — Break It Down

The story goes that Einstein once said compound interest is “the most powerful force in the universe.” He probably didn’t actually say that, but the theory isn’t that far off. In its most simplified version, compound interest is often explained as “interest on interest”—a sort of perpetual motion machine in which money begets more money.

Depending on the context, compound interest is either punishing or pretty freakin’ sweet. Here’s the good, the bad, and the ugly on this oft-misunderstood financial power.

## The basics

At its core, compound interest is interest that adds to the principal balance with a snowball effect. You start with the principal. Interest is charged on that balance, giving you a bigger total. Since the balance is now larger, there’s more money to charge interest on. Interest charges kick in again, adding even more money to the balance, and so on.

One area where most of us have seen compound interest at work is our credit card bills. It’s why your statement likely shows an estimated time to pay off your balance many months (or years) in the future if you only make the minimum payment each month. The longer you take to pay off the total, the more time interest has to accrue and compound, pushing your $0 balance goals further and further away.

But compound interest isn’t just a credit card thing. It’s present on loans—especially home mortgages—too. And fortunately, compound interest can work for you as well, if you stash cash in investment funds, high-interest bank accounts, money market accounts, and CDs.

## The difference between simple and compound interest

To get into compounding, let’s start with a simple lesson.

“A great example is someone starting with $10,000 who happens to find a magical investment that pays 10 percent, annually,” explains Ryan Farnung, a planning research assistant at GPS Financial, an investment and financial planning company in Pittsford, New York. “Let's say they invest for five years. Many people would assume that their earnings are $5,000 (five years times $1,000 in interest on the $10,000 principal), but that's not how it actually works.”

Using the example above, if you only earned $5,000, that would be simple interest, not compound interest. The total interest earned actually comes to $6,105.10. Here’s how we get there:

In the first year, you make $1,000.

That $1,000 is added to your principal.

Your principal is now $11,000.

The following year you make 10 percent of $11,000, which is $1,100.

Add that to the original principal, and you start with $12,100 in the third year.

In the third year, you make $1,210 in interest.

Add that to the principal, and you start with $13,310 in the fourth year.

In the fourth year, you will make $1,331 in interest and end with a principal of $14,641.

By the fifth year, you make an additional $1,464.10 in interest for a $16,105.10 final principal.

Of course, an even easier way to sort this out is using an online calculator like the one at the U.S. Securities and Exchange Commission’s website.

## Your mileage may vary

It’s important to note that compound interest rates vary depending on what kind of investment account (or type of debt) you have. You’ll be lucky to get a typical, run-of-the-mill savings account from the bank with an APY (annual percentage yield) for more than 1 percent—and that’s the so-called “high yield” account. The average savings rate across the nation was a paltry 0.06 percent this June.

Similarly, a 10 percent return on a retirement account is “magical” thinking, as Farnung put it. Retirement accounts are tied to the stock market, so the rate of return fluctuates. Because of that fluctuation, there is no real across-the-board average return rate for retirement accounts and predictions vary. Bloomberg reported investors could expect a 4.6 percent return rate over the next 10 years.

“While interest payments and dividend payments occur with regularity, market appreciation fluctuates drastically, so there really isn't a set schedule in which the interest compounds,” Farnung says.

## When the force of compound interest turns against you

Compound interest is freakin’ great when you’re using it for an investment. Unfortunately, many people will first encounter compound interest working its magic on their debt. For example, if you instead owed a 10 percent compound interest annually for a five-year $10,000 loan, you would have to pay that extra $6,100 in interest.

But let’s go back to the most common financial tool that uses compound interest: the credit card. Credit card interest isn’t compounded yearly; it’s compounded daily. So, let’s say you have a $4,000 debt on a credit card with an APR of 22 percent. Here’s how you figure out how much you’re paying each day:

To get your daily interest rate, first divide your APR by either 360 or 365. (The exact figure varies by card and issuer.) Assuming it’s a 365-day term.:

22 divided by 365 = 0.0603%

To figure out how much you’ll owe the issuer each day, multiply that percentage by your $4,000 balance. (Don’t forget to move the decimal!)

0.000603 multiplied by $4,000 = $2.41

At $2.41 per day, the issuer will charge you $72.30 at the end of a 30-day month. That $72.30 is plopped back into the principal, and you start the next month with a $4,072.30 balance—provided you haven’t made additional payments or purchases.

So if you paid $100 a month on your $4,000 balance, it would take you 73 months (about six years) and a total of $7,325 to pay it off.

To make sure you’re on the right side of compound interest (and making the most of it if you are) follow these simple rules: If you’re investing into a compound interest-bearing account, invest regularly over a long period. If you’re paying off a compound interest loan, get to $0 ASAP to avoid paying a ton of interest. And no matter what debt or investment, make sure you know whether that interest is accruing daily, weekly, monthly, or annually.