5 Min Read | December 30, 2022

What is Compound Interest & How is it Calculated?

Understand what compound interest is and how it works. Make interest work for you and grow your finances more quickly.

This article contains general information and is not intended to provide information that is specific to American Express products and services. Similar products and services offered by different companies will have different features and you should always read about product details before acquiring any financial product.

At-A-Glance

Compound interest is simply about earning (or paying) “interest on interest.”

Understanding how compound interest works and making it work for you can have an enormous impact on your finances.

The younger you are, the more time you have for compounding to work its magic.

But compound interest on loans can generate escalating debt balances, which sometimes gets borrowers into trouble.

“My wealth has come from a combination of living in America, some lucky genes, and compound interest.”

—Investor Warren Buffet1

Even if you’re not one of the richest people in the world, you too can benefit from understanding compound interest.

What is Compound Interest?

Compound interest is interest calculated on the sum of the initial amount of either an investment or a loan plus any interest already accumulated. Since compound interest generates “interest on interest,” it makes a sum grow at a faster rate than simple interest.2 Whether this acceleration is good or bad depends on whether you’re collecting compound interest on an investment or paying it out as a borrower.

Compounding is widely used to calculate interest for most investment vehicles, loans (such as mortgages, auto, and small-business loans), and credit cards. Another, seldom used method is “simple interest,” which is discussed in “What is an Interest Rate?

How is Compound Interest Calculated?

The same formula for compound interest is used for an investment or a loan, but the impact on your wallet is very different. The key components in the equation are compounding frequency and time (length of the loan or investment). Compounding frequency (N) can be monthly, weekly, or even daily. When these variables are higher, the impact is greater.

The formula for compounding looks like this:3

A = P (1 + r/n) (nt)

• A = the total future value of principal + interest.
• P = the beginning amount borrowed or invested, or principal.
• r = the stated annual interest rate, expressed as a decimal (for credit cards, it’s also the Annual Percentage Rate, or APR).
• n = the number of compounding periods per year.
• t =the number of years money is invested or borrowed.

Many online calculators can do the math for you, such as the one on the Securities and Exchange Commission (SEC) website.

Compound Interest in Investing

In the case of an investment (or bank deposit), the compound interest method assumes that when you earn interest it is reinvested and added back to the beginning principal rather than paid out. Interest is then earned on the new higher balance, reinvested again, and so on.

Most banks pay compound interest on deposits on a monthly basis, but others compound daily, so it’s worth asking your bank about it. Retirement and college savings accounts rely heavily on the power of compounding, and they’re often turbocharged by compounding balances before taxes are taken out.

The younger you are, the more time you have for compounding to work its magic. So when it comes to retirement accounts, it’s generally a smart idea for individuals to start saving early in their careers, even if it’s just 1% of each paycheck. That small bit can make a noticeable difference over time.

For example, the accompanying table shows a simple example of how compound interest works on a \$100 investment that earns, for simplicity’s sake, 10% interest. You can see how the small improvements after one or two years of compounding can build to a significant impact after 10 or 20 years, especially with a monthly or daily compounding frequency. Your initial \$100 could be worth up to \$738.70 in 20 years!

 Yearly Monthly Daily 1 Year \$110 \$110.47 \$110.52 2 Years \$121 \$122.04 \$122.14 10 Years \$259.37 \$122.04 \$271.79 20 Years \$672.75 \$732.81 \$738.70

Compound Interest in Borrowing

In the case of a loan, compounding accumulates interest on the outstanding principal plus the interest that was not paid during the previous compounding period. Compounding interest can generate escalating debt balances, which can sometimes get borrowers into trouble. When loans are compounded frequently, left outstanding for longer periods, or their interest/balances are not paid in full, the impact of compounding can be costly to the borrower.

To illustrate the effect of compounding on a loan, consider the example of a \$10,000 loan at a nominal interest rate of 5% for a term of one year.

• Using the simple interest method, the borrower pays back the principal plus \$500 in interest charges.
• If, however, the loan compounds interest quarterly, the borrower would pay \$510 in interest charges at the end of the same year.
• If compounded monthly, the interest charge would be \$512.
• If compounded daily, \$513.

These seemingly small differences would grow rapidly for loans of longer terms. The longer the term, the larger the principal, or the higher the interest rate, the more drastic the differences will be.

Credit card issuers typically compound interest daily and charge it monthly. For this reason, carrying an outstanding balance on a credit card can become expensive.

What is Continuous Compound Interest?

You can think of continuous compound interest as extreme compounding. The number of times per year that interest is compounded using this method is infinite, and its calculation is very complex. Continuous compounding exists mostly in the world of financial derivatives, with very few real-world applications for consumers. Credit card companies generally compound interest daily, not continuously.

The Takeaway

Understanding how compound interest works and making it work for you, while limiting the extent to which it works against you, can have a significant positive impact on your household budget—and financial future.

Kristina Russo is a CPA and MBA with over 20 years of business experience in firms of all sizes and across several industries, including media and publishing, entertainment, retail, and manufacturing.

All Credit Intel content is written by freelance authors and commissioned and paid for by American Express.

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