Compound interest is nothing more than basic arithmetic, but this financial rule has important implications for both saving and borrowing. It could help you build your savings account over time or rack up runaway debt, if you let it.
In an investing context, compound returns work similarly to compound interest and could potentially help you grow a sizable retirement nest egg over time.
Here’s how compound interest works — and how to make it work for you.
What is compound interest?
Compound interest is when a bank charges or pays interest on both an initial amount of money and the interest it accrues. In a borrowing context, a bank might charge compound interest on a line of credit. For instance, you’ll pay interest on a credit card balance if you don’t pay it off each month. Left unpaid, those interest charges will compound each month, increasing the amount you owe and potentially making it difficult to pay off your balance. In this case, compound interest can work against you.
In a savings context, a bank might offer a 5-year CD account with a generous annual APY. So when you make an initial deposit into that account, the bank will pay you interest for the privilege of holding your money. Over the course of that 5-year term, your account balance will grow thanks to compound interest. In this example, compound interest can work in your favor.
Like all interest payments, compound interest only applies to borrowing and saving. This can lead to a bit of confusion when it comes to finance and how to invest money. For example, when you open a savings account, the bank pays you a rate of interest. This happens because the bank borrows your money while it sits in your account, and they pay you for that privilege.
Compound interest shouldn’t be confused with the concept of compounding returns, which can look similar from a distance. For example, many investors in the stock market will reinvest any dividends they collect in their portfolio. This can create a compounding return, as your gains themselves could potentially lead to future gains. However, it’s important to remember that all investments come with the risk of loss. While compound interest can lead to compound returns, an interest payment applies only to the structured, obligated payments of a debt instrument.
In a borrowing situation, a lender will typically set one of two main types of interest rates:
1. Simple interest
As its name suggests, this is the basic form of an interest payment. It means that you pay a flat rate applied to the loan every payment period. Say you take out a $10,000 loan with a simple interest rate of 5% per year. You would pay $500 in annual interest on this loan, or $41.67 in interest each month.
2. Compound interest
With compound interest, the lender charges interest on the loan with payments due at set time periods. However the lender also periodically “compounds” the loan, which means that it adds any accrued interest to the principal for the purpose of calculating all future interest payments.
Say you take out a $10,000 loan with an annual interest rate of 5 percent, compounded monthly.
This means that if you missed your first month’s payment, you would owe $41.67 in interest ($10,000 * 0.05 * 1/12), or $10,041.67 total. In the second month, if unpaid, the interest is compounded (10,041.67 * .05 * 1/12 = 41.84), so you’d now owe $10,083.51. In this way, you have paid interest on the interest.
How does compound interest work?
As we note above, when interest compounds, that means that the lender applies each new interest calculation to both the remaining loan (the principal) and any existing interest on the account. While this is problematic when it comes to debt and personal finance, it can be outstanding when it comes to saving and investing.
For example, say you buy into a mutual fund built out of corporate debt (bonds). This fund pays an average interest rate of 7% per year, a number based on the combined interest rates of all the underlying bonds in its portfolio. You put $10,000 into this mutual fund and instruct your broker to roll all returns back into new shares, so every time you get an interest payment your stake in this fund grows. Here’s how your initial investment would grow over time, assuming interest is compounded annually:
- Year one: $10,700 ($10,000 * 1.07)
- Year two: $11,449 ($10,700 * 1.07)
- Year three: $12,250.43 ($11,449 * 1.07)
Let’s skip ahead a bit:
- Year 13: $24,098.45
- Year 14: $25,785.34
- Year 15: $27,590.32
As you look at the example above, it isn’t just the balance in your account that grows. The rate of change itself also increases over time.
During the first few years of this account, you add $700 or so per year, so the growth you see is probably not that different from simple interest. But by the fifteenth year of this account, it’s growing by $1,805 per year, more than 2.5 times its original rate of growth.
While your interest rate remains the same (always 7%), the rate at which your balance grows accelerates. Let’s look at what happens if you hold this investment even longer:
- Year 23: $47,405.30
- Year 24: $50,723.67
- Year 25: $54,274.33
Now your account is growing by approximately $3,500 each year. By year 25, your new balance on that $10,00 initial investment is $54,724.33. This is the strength of compound interest — and how it can sometimes seem like magic.
To find out how you can build an account like this, see our picks for the best brokerage accounts.
How to calculate compound interest
Interest can compound on any schedule based on the nature of your contract or the terms of your account. In the mutual fund example above, the interest is compounded annually which is typical for this class of investment though quarterly-compounding (four times a year) is also common. Some of the better high-yield savings accounts compound interest daily. For the calculation example below, interest is compounded monthly, a common time interval for savings and investment accounts.
You can calculate compound interest using the following compound interest formula. It’s worth noting that this formula can be used to calculate compound interest in a savings or lending context as well as compound returns in an investing context:
A = P * (1 + r/n)^nt
- A = Amount
- P = Principal
- r = Interest rate (expressed as a decimal)
- n = Number of times interest is compounded per unit of time (t)
- t = Time
It’s important to use the same time period for all parts of this formula. For example, if you are measuring t in years, n should be the number of times interest is compounded annually.
Let’s say you’re calculating the growth of a $10,000 principal at a 5 percent annual interest rate, compounded monthly for 25 years. Your formula would look like this:
- A = 10,000 * (1 + 0.05/12)^(12*25)
Note the relationship between n and t. Since we are calculating interest over a period of years, we calculate the number of times interest compounds each year. In this example, the interest is compounded monthly, so 12 times per year, for 25 years, hence 12 * 25 = 300. So the interest has been compounded and added to the principal 300 times.
- A = 10,000 * (1 + 0.0041667)^(12*25)
- A = 10,000 * (1.0041667)^300
- A = 10,000 * 3.48132
- A = $34,813
At the end of 25 years, your initial $10,000 deposit will have grown to $34,813 without your adding any additional deposits beyond the interest earned. This is how your money goes to work for you, instead of you working for your money, when you take a long-term approach to saving and investing.
If you prefer a quick and simple compound interest calculator, you can also use the Rule of 72 to roughly determine how long an account will take to double in value.
- Time to double = 72 / interest rate
So, in our example above, we would get a rough calculation of:
- Time to double = 72 / 5
At five percent interest, compounded annually, it will probably take a little more than 14 years (72 / 5 = 14.4) for this account’s balance to double.
How to make compound interest work for you
Compound interest is one of the most powerful financial tools in the market. Understood poorly, it has the potential to make debt unmanageable. In particular, credit card balances can grow quickly if you don’t pay them off each month. Left unpaid, these balances could easily spiral out of control because of compounding interest charges.
However, used wisely, compound interest could help you build your savings over time. Saving for retirement can depend on this. Taking advantage of compound interest means taking a few important steps:
Start saving early
As we discussed above, compound interest typically has little impact in its early years. For a standard account, in which interest compounds monthly or annually, you will rarely see much difference between compound and simple interest in the first few years. It takes time for compound interest to really make a difference.
To take advantage of compound interest, it’s a good idea to start saving early.
Understand compounding frequency
Compound interest is defined by compounding periods. In other words, how often is the interest on your account compounded back onto your principal?
An account with interest that compounds every month will have different financial ramifications than one that compounds annually. So it’s good to know how often interest compounds on your accounts, especially if you’re interested in understanding the future value of your savings.
Understand potential returns
Finally, the returns on an interest-bearing account with regular compounding can be difficult to fully predict when doing the math in your head. Take a few minutes to run the numbers on what your account will generate over the lifetime of your investment, or visit this calculator provided by the SEC. By understanding your potential returns today, you will be better prepared to plan for tomorrow.
What will $100k be worth in 20 years?
As an example, let’s consider a $100,000 initial deposit into a no-cost ETF, tracking the S&P market index from 2000-2020 with dividends reinvested quarterly. Note that the S&P returned an average of 8.2% annually during this period, despite economic downturns following the 9/11 attacks and the 2008 recession.
By plugging these numbers into our compound interest formula, we get:
- A = P * (1 + r/n)^nt
- A = 100,000 * (1 + .082/4)^4*20
- A = 100,000 * (1.0205)^80
- A = 100,000 * 5.0704
- A = 507,040
With this investment, you’d end up with roughly $507,040 — five times your initial investment — at the end of the 20 years, thanks to compounding returns.
Note that the past performance highlighted in the example above is not a guarantee of future performance. Nobody can predict how the stock market will perform in the next 20 years. That said, this type of hypothetical modeling can be useful if you’re interested in understanding the possible outcomes of your investments. Just remember that all investments come with the risk of loss.
Is compound interest a good thing?
In a savings and investment situation, compound interest and compound returns are the chief ways to build stable wealth through investment. While it’s always fun to hit it big on a single stock or speculative asset, most investors generally see gains by steadily building wealth and letting it grow on its own earnings. Though it’s important to remember that you can lose money too.
From a debt-based perspective, however, compound interest can be disastrous. When someone’s credit card or student loans get on top of them, compound interest is often a contributing factor. Left unpaid, it can cause personal debt to grow to the point where many people end up paying more in interest than they took out on the original loan.
Can compound interest make you rich?
Taking advantage of compound interest could potentially be a good way to build wealth. However, there’s often a correlation between the potential rate of return and risk level. In a savings context, putting money into a traditional savings account is considered pretty low risk, but the annual percentage yield (APY) on a traditional savings account is just 0.07% (as of Apr. 1, 2021). Given this, it’s unlikely you’ll get rich off the compounding interest in your savings account.
In an investing context, bonds could be considered one of the safer investments on the market, but they also tend to pay some of the lowest rates of return. Stocks have a higher potential for return yet are inherently riskier than bonds. While it’s possible to build wealth with smart investments, it’s also possible to lose money.
The bottom line
Compound interest can be a very powerful tool when it comes to savings, and similarly, compounding returns can be a powerful tool in investing. As your account grows, your returns on that account could potentially grow too. Given time, this is one of the best ways to securely grow wealth on the market today. If you are interested in taking advantage of compound interest, check out our picks for the best savings accounts.