How Does Compound Interest Work?

You'd think that to accumulate a lot of money, whether in a savings account, retirement savings plan, or brokerage account, you'd need to consistently put a lot of money in there. But if you save and invest your money wisely, and do so over a long period of time, you could wind up pleasantly surprised at the level of wealth you achieve to meet your financial goals.

If the idea of watching your money grow before your eyes sounds appealing, then it pays to take advantage of the power of compound interest and returns. Here, we'll review what compounded growth entails and show you how a series of relatively modest contributions to a savings or investment account can evolve into a substantial sum over time.

How does compound interest work?

At its core, compounding is the concept of earning interest on interest.

Imagine you put an initial deposit of $1,000 into a savings account paying 2% interest. That means that after a year, your balance will grow to $1,020 (assuming, of course, that you don't put any more money in or take any out).

Now here's the cool part: If you keep that money where it is, you'll continue earning interest on not just the initial $1,000 you put in, but also on that $20. Assuming your interest rate stays the same, you'll earn $20.40 in interest in your second year of having that money in that account.

What are the benefits of compound interest?

The upside of compounding? It can make you wealthy. When you benefit from compound interest, you earn money without needing to do any extra work. Then, the money you've earned continues earning even more. Before long, even if you only saved a small amount, you'll see your savings grow.

The downside: If you're being charged compound interest -- say, with a credit card -- you'll lose money quickly.

How does compound interest work in the stock market?

Imagine you're looking to invest your money for a long-term goal, like retirement, and you put $100 a month into a brokerage account or IRA instead of a bank account. A savings account today might pay just 2% interest, but investing in the stock market has historically delivered more like a 9% average yearly return. To be a bit more conservative, we'll use a 7% return for our calculations. The following table shows how much money you could wind up with, depending on how many years you save for:

Invest $100 a Month for This Many Years	Which Means Putting in This Much Money	And This Will Be Your Ending Balance
3	$3,600	$3,859
5	$6,000	$6,902
10	$12,000	$16,581
15	$18,000	$30,157
20	$24,000	$49,198
25	$30,000	$75,904
30	$36,000	$113,360
35	$42,000	$165,894
40	$48,000	$239,577
45	$54,000	$342,920

Data source: Author calculations.

You'll notice that as you get further down the table, the numbers don't just get bigger; they represent increasingly larger gains. Our top row shows that in three years, $3,600 in out-of-pocket contributions to an investment account turned into $3,859, representing a $259 gain. If we look at our third row with a 10-year investment window, we see that $12,000 in out-of-pocket contributions turned into $16,581, representing a $4,581 gain. And in our very bottom row, we see that $54,000 in contributions turned into $342,920 over 45 years, leaving us with a very substantial and impressive $288,920 gain.

The compounding effect is the reason these gains are possible.

One thing to keep in mind about the above table is that it assumes that interest is compounded annually -- meaning, once a year. Different accounts work differently, and depending on your financial institution, your interest will compound more than once a year -- say, semiannually or quarterly. The more frequently compounding happens in your account, the more you gain.

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How long does it take for compound interest to work?

As the table above illustrates, the longer a savings or investment window you have, the more you stand to benefit from compounding. In other words, while you can capitalize on compounding by investing for just a few years, your gains will be higher if your returns compound for 20 years instead.

How compounding can work against you

We just saw that compounding could help you turn a series of relatively small contributions to an investment account into quite a large sum, especially with a longer window of time. But compounding can also work against you, particularly when it comes to credit card debt.

When you rack up a credit card balance that you fail to pay off by the time it comes due, your credit card company will start charging you interest on the sum you continue to owe. But over time, you'll also be charged interest on that interest, not just on the initial balance.

Let's say you rack up a $1,200 credit card balance, and you pay it off in $100 increments each month so that it's gone in a year and two months. If your credit card's annual interest rate is 18%, you'll wind up losing $133 in interest charges -- not great, but not terrible. But if you only manage to pay off $50 a month, it will take you 30 months in all and you'll end up losing $298 to interest charges. But notice that you're not just paying two times that initial $133 in interest charges, which would be $266. You're paying more interest than that, because you'll continuously be charged interest on the interest you owe as well as your principal balance.

This breakdown shows what happens when you pay a $1,200 credit card off over time in $50 increments:

#	Payment	Interest	Principal	Balance
				$1,200
1	$60	$18	$42	$1,158
2	$60	$17	$43	$1,115
3	$60	$17	$43	$1,072
4	$60	$16	$44	$1,028
5	$60	$15	$45	$984
6	$60	$15	$45	$938
7	$60	$14	$46	$892
8	$60	$13	$47	$846
9	$60	$13	$47	$799
10	$60	$12	$48	$750
11	$60	$11	$49	$702
12	$60	$11	$49	$652
13	$60	$10	$50	$602
14	$60	$9	$51	$551
15	$60	$8	$52	$499
16	$60	$7	$53	$447
17	$60	$7	$53	$394
18	$60	$6	$54	$339
19	$60	$5	$55	$285
20	$60	$4	$56	$229
21	$60	$3	$57	$172
22	$60	$3	$57	$115
23	$60	$2	$58	$57
24	$57	$1	$57	$0

Source: 360 Degrees of Financial literacy.

Now, remember how earlier we said that the more frequently interest compounds, the more it amounts to? Well, some credit card issuers (though not all) compound interest daily, which means for each day you carry a balance, you're charged interest on interest. Ouch. Therefore, while compound interest can be a powerful tool that works for you, it can also very much work against you.

What is the formula for compound interest?

If you really want to get into the math behind compound interest, here's the formula you need to know:

A = P (1 + r/n) ^ n*t

Here's what these variables mean:

A is the sum you'll end up with
P is your principal contribution
R is your annual interest rate, written in decimal format
N is the number of compounding periods per year (for example, interest that compounds annually would be 1)
T is the number of years that your money compounds

Now, say you invest $3,000 at an annual 7% interest rate that compounds once annually over 10 years. Here's what you'd end up with:

3,000 (1 + 0.07/1) ^ 1*10

which becomes

3,000 (1.07) ^ 10 (that ^ means "to the power of," in case you're confused)

which then becomes

3,000 (1.967)

which equals $5,901, which is the total amount your investment will grow to, representing a gain of $2,901. Sweet!

Make compound interest work for you

The best way to take advantage of compound interest is to give yourself as many years as possible to build wealth. Many people who retire as millionaires don't have six-figure incomes or family trust funds. Rather, they start saving and investing at a young age, and continue doing so consistently over many years. If you sock away just $300 a month and invest it at an average annual 7% return, you'll wind up with just over $1 million over 45 years.

It's equally important to not fall victim to compounding. That means understanding how compound interest applies to credit cards and avoiding scenarios where you're carrying a balance for too long. If you make a point to use compound interest to your benefit and don't let it work against you, you'll position yourself to acquire a lot of wealth in your lifetime -- without even having to work too hard for it.

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