How Compound Interest Works and How To Calculate It

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.

Here’s how compound interest works — and how to make it work for you.

What is compound interest?

Compound interest is when interest accrues on the principal — the initial amount — as well as on previously accrued interest. Compound interest can apply to both borrowing and saving money.

When a bank charges compound interest on debt, the interest owed is calculated based on the principal plus any existing interest. Compounded this way, debts can start to get out of control very quickly. Credit cards and loans often charge compound interest.

You can also earn compound interest on savings, where the bank pays you interest based on your principal as well as the interest you’ve already earned. This makes it easier to amass much more wealth over time than you would if the interest weren’t compounded. You can earn compound interest on savings accounts (including high-yield savings accounts), certificates of deposit (CDs) and money market accounts.

How compound interest works

When interest compounds, the lender applies each new interest calculation to both the remaining loan (the principal) and any existing interest on the account.

Here’s an example. Say you buy shares of a mutual fund paying an average interest rate of 7% per year. You put $10,000 into this mutual fund and reinvest the earnings.

Here’s how your initial investment would grow over time, assuming interest is compounded annually:

• Year one: $10,700 ($10,000 x 1.07)
• Year two: $11,449 ($10,700 x 1.07)
• Year three: $12,250.43 ($11,449 x 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 in this example remains the same at 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: annually, quarterly, monthly, even daily with certain high-yield savings accounts. In the mutual fund example above, the interest is compounded annually.

You can calculate compound interest using the following compound interest formula. 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 x (1 + r/n)^nt

Where:

• 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.

Example of calculating compound interest

Let’s say you’re calculating the growth of a $10,000 principal at a 5% annual interest rate, compounded monthly for 25 years. Your formula would look like this:

A = 10,000 x (1 + 0.05/12)^(12x25)

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: 12 * 25 = 300. So the interest has been compounded and added to the principal 300 times.

• A = 10,000 x (1 + 0.0041667)^(12x25)
• A = 10,000 x (1.0041667)³⁰⁰
• A = 10,000 x 3.48132
• A = $34,813

At the end of 25 years, your initial $10,000 deposit will have grown to $34,813 without adding any additional deposits beyond the interest earned.

Rule of 72 for estimating compound interest

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 5% interest, compounded annually, it will probably take a little more than 14 years (72 / 5 = 14.4) for this account’s balance to double.

Compound interest vs. simple interest

In a borrowing situation, a lender will typically set one of two main types of interest rates: compound or simple.

Simple interest 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.

Simple interest does not use previously earned interest in its calculations, unlike compound interest.

How to make compound interest work for you

Compound interest is one of the most powerful financial tools in the market. Unchecked, it has the potential to make debt unmanageable. Credit card balances in particular can grow quickly if you don’t pay them off each month, due to compounding interest and relatively high interest rates.

However, used wisely, compound interest can help you build your savings over time. Saving for retirement is a great example of starting early and letting compound interest do the heavy lifting. Here are a few ways to take advantage of compound interest.

Start saving early

As we saw in the example above, compound interest can have little impact at the beginning. For a standard account where interest compounds monthly or annually, you will rarely see much difference between compound and simple interest in the first few years. But after many months or years, the balance begins to grow exponentially, even without additional investments.

Understand compounding frequency

Compound interest is defined by compounding periods. In other words, how often is the interest on your account compounded?

An account with interest that compounds every month could earn more faster 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.

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Bottom line

Compound interest can be a very powerful tool when it comes to savings and investing (and a major obstacle when it comes to debt). As your account grows, your returns on that account could potentially grow too.

Given time, compound interest is one of the best ways to 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.