What is Compound Interest?

There are many types of interest and corresponding formulas for calculating interest. Two of the most common types of interest are simple interest and compound interest. Compound interest is used in both debt and investment products. There are several factors to understanding how compound interest works, as well as a formula for calculating compound interest. Read on to learn about compound interest.

What is Compound Interest?

According to Investopedia.com, compound interest is the interest on a loan or deposit calculated based on the initial principal amount and the accumulated interest of previous periods. In simpler terms, compound interest generates “interest on interest”, which allows the sum of the loan or deposit to grow exponentially faster through the technique of compounding. Albert Einstein once described compound interest as the eighth wonder of the world, stating “he who understands it, earns it; he who doesn't, pays for it.”

Understanding Compound Interest

There are a few key factors to consider when calculating compound interest:

• Interest. The interest rate earned on an investment product or charged on a loan. 
• Starting principal. The initial amount that was deposited or borrowed.
  
• Frequency of compounding. The pace at which interest is compounded—daily, monthly, or annually—determines how rapidly a balance grows.
  
• Duration. The length, or term, of a loan or investment product.
  
• Deposits and withdrawals. Funds coming into or out of an account can impact how much interest is earned or paid.

Examples of Compound Interest

Compound interest can either help or hurt you, depending on whether you’re saving or borrowing money.

• Savings accounts, certificates of deposit (CDs), and money market accounts. When a deposit is made into an account that earns interest, the interest will be deposited into the account and added to the principal balance, helping the balance grow over time. Savings accounts, CDs, and money market accounts are all low-risk accounts with compounding interest.
  
• 401(k) accounts and investment accounts. Earnings in a 401(k) and other investment accounts also compound over time. The percentage that stocks gain from day to day are calculated based on their performance the day before, meaning they compound each business day. If you reinvest your dividends and make regular deposits, you can help your balance grow even faster.
  
• Student loans, mortgages, and other personal loans. Compound interest works against an individual when they take out a loan. When borrowing money, interest is accrued on any money that isn’t paid back. If the interest charges are not paid within the period stated in the loan, they’re “capitalized,” or added to the initial loan balance. After that, future interest accrues on the new, larger loan balance. 
  
• Credit cards. Each month, interest is charged on credit card balances. If additional charges are not added to the card and the accrued interest is paid each month, the balance will remain the same. But if enough isn’t paid to cover the month’s new interest, it will be added to the balance of the credit card. Then, the next month’s interest is calculated based on that higher amount. Over time, this can cause the balance to skyrocket.

How to Calculate Compound Interest

There are a few ways to calculate compound interest. The easiest way is to have an online calculator do the math for you. Another way is to use a formula in Microsoft Excel. Either way, it’s helpful to see the moving parts to truly understand how compound interest works.

Here’s the compound interest formula with an explanation of each component:

A = P (1 + [r / n]) ^ nt
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial deposit or the initial credit card balance)
r = the annual rate of interest (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years (time) the amount is deposited for

It’s important to note that the annual interest rate is divided by the number of times it’s compounded in a year. This gives you the daily, monthly, or annual average interest rate, depending on compounding frequency.

Here’s how that plays out with numbers: Let’s say you put $10,000 into a savings account paying 3.75% interest. The account is compounded monthly for 20 years. In this situation, you know P ($10,000), r (.0375), n (12), and t (20). Now, let’s put those in the compound interest formula.

A = P (1 + [r / n]) ^ nt
A = 10,000 (1 + [.0375 / 12]) ^ (12 * 20)
A = 10,000 (1.003125) ^ (240)
A = 10,000 (2.11452576062)
A = 21145.2576062 = 21145.26

In 20 years, you’d have about $21,145 in the account. That includes your $10,000 initial deposit and $11,145 in interest.

Things to Keep in Mind with Compound Interest

• The higher the interest rate, the more money that is earned or the more money that is owed.
  
• Make sure you understand how often interest compounds (daily, monthly, annually, etc.).
  
• The pace at which the principal balance is built up or the loan is paid down makes a big difference in the long-term.
  
• The longer money is left in a savings account or the longer debt is held onto, the longer it has to compound and the more the account will earn—or owe.

Compound interest is a fundamental financial concept that plays a crucial role in the growth of investments and debts. It allows individuals to earn or owe interest not only on their initial principal amount but also on any accumulated interest over time. With the power of compounding, even small investments made early on can grow significantly over the long-term. As such, understanding and utilizing compound interest can be an effective strategy for achieving financial goals and building long-term wealth. However, it's important to keep in mind the associated risks, such as the potential for losses, and to carefully consider one's investment choices and financial circumstances before making any decisions.