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How Does Compound Interest Work?

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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 away. But if you save and invest your money wisely over a long period, you could wind up pleasantly surprised at the level of wealth you achieve.

If the idea of watching your money grow before your eyes sounds appealing, 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 that pays 2% interest. That means after a year, your balance will grow to $1,020 without adding any more money.

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, for a balance of $1,040.40.

After 40 years in that account, earning the same interest, your $1,000 will grow to $2,208.04 -- more than double your initial savings, with no extra investment or work.

Generally, you don't just sock away a lump sum of money and come back to it in 40 years. In reality, most people save or invest some each week or month. So your savings grows with your principal -- the money you put in -- plus the interest that continues to compound as the initial balance grows with both principal and interest.

What are the benefits of compound interest?

The upside of compounding? It can grow your money. Interest means you earn money without needing to do any extra work. Then, the money you earned continues earning even more -- that's compounding. Your money continues to grow, whether you continue to add to it or not.

The downside: If you're being charged compound interest -- say, for a credit card balance -- your debt can grow just as easily.

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 high-yield savings account might pay just 2% interest.

By contrast, investing in the stock market has historically delivered a 10% average yearly return -- though a return in any given year fluctuates quite a bit. To be 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 continue to save:

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.

Notice 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.
  • Look at the third row with a 10-year investment window. A $12,000 out-of-pocket contribution turned into $16,581, representing a $4,581 gain.
  • In the very bottom row, $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 makes these gains possible.

Note that these calculations assume interest is compounded annually -- meaning the interest you earn is only added to your balance once each year. So, for a full year, you only earn interest on your principal investments.

Accounts compound at different intervals. Savings accounts typically compound daily or monthly -- so interest earned on your balance is swept into your balance to earn interest the very next day or every 30 days. Some investment accounts compound interest semi-annually or quarterly. The more frequent compounding happens in your account, the more you gain.

That total rate of gain per year, with these compounding intervals taken into account, is called the annual percentage yield (APY). When you're charged interest, it's the annual percentage rate (APR).

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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 before you touch your savings, the more you stand to benefit from compounding.

You can capitalize on compounding by investing for just a few years, but your gains will be higher if your returns compound for 20 years instead. That's why you're so often encouraged to start saving for retirement as early as possible. The earlier you start saving, the less principal you have to invest to end up with the same amount.

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 long window of time. But compounding can work against you when you're charged interest on debt.

It's particularly insidious when it comes to credit card debt.

You can use a credit card for purchases without paying interest as long as you repay the balance by the time it's due. Any remaining balance on the card -- even if you've made the minimum required monthly payment -- accrues interest. Over time, that interest is added to what you owe, and it also accrues interest.

Here's an example: Say you make $1,200 in credit card purchases this month, and you make $100 payments each month (and don't make any other purchases on the card in the meantime). If your credit card's annual interest rate (or APR) is 18%, you'll pay $133 in interest and pay off the balance in 14 months.

If you instead make $50 payments each month, you'll pay $298 in interest and take 30 months to pay off the balance. By paying half the amount, it takes you more than twice as long to repay what you owe, and you pay more than twice the amount of interest -- because of compounding.

This breakdown shows what happens when you pay a $1,200 credit card off over time in $60 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.

Remember how earlier we said 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 past the due date, you're charged interest on interest.

While compound interest can be a powerful tool that works for you when you're saving, it can also very much work against you when you're spending and borrowing.

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 your money compounds

Say you invest $3,000 at a 7% APY 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 invest just $300 a month and get an average annual 7% return, you'll wind up with just over $1 million after 45 years.

It's equally important to not fall victim to compounding. That means understanding how compound interest applies to debt 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 make your money work for you throughout your life.

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