What is Compound Interest?

Compound interest is interest calculated on the principal amount, as well as the accumulated interest from previous periods. Whenever a principal's earned interest is compounded, interest is paid on that new amount, not just the loan's principal. This is different from simple interest, for which earned interest is only ever calculated based on the principal.

Although compound interest is always calculated based on the principal amount (the initial size of the deposit) as well as the interest it accumulates over time, it can compound at different rates (for example, daily, monthly or quarterly).

Savings products like traditional savings accounts, money market accounts, CDs, and savings and CDs in retirement accounts all may compound interest.

Let's take a deeper look at how compound interest works, as well as some example calculations and types of bank accounts that may use it.

Formula for compound interest

The compound interest formula typically considers:

• Your principal
• Interest rate
• Time and compounding frequency, which are typically daily, monthly or annually

The formula below will tell you how much interest you'll earn over that period.

The compound interest formula is:

Initial principal amount multiplied by (1 plus the annual interest rate, divided by the number of compounding periods in a year, raised to the number of compounding periods multiplied by time)

OR

A = P (1 + r/n) ^(nt)
P is your principal (initial deposit)

r is the annual rate of interest as a decimal

t is the length of time the principal is on deposit

n is the number of times interest is compounded per unit of t

A is the future value you will have at the end of the time period

You can use the formula to explore different scenarios and see how compound interest can make a real difference in your savings and life goals.

How does compound interest work: daily, monthly and yearly compounding

Example of interest compounding annually

Let's see examples of how the compounding interest formula works using a hypothetical rate.

Say you deposit $10,000 in a savings account that earns a 2.3%* annual rate of return. Use the compound interest formula to calculate the amount you would have at the end of a savings period for different compounding options.

A = P (1 + r/n) ^(nt)

Starting with a balance of $10,000 and a 2.3%* annual rate of return, after one year you can end up with as much as $10,233 in a savings account.

Notice how the more frequently your interest is compounded, the more interest you earn.

What could happen if you save that $10,000 for 5 years instead? That initial deposit can grow via compounding by more than $1,200 with a 2.3%* annual rate.

If you really want to reap the advantages of compound interest, consider the potential impact of regular contributions. For example, by contributing $100 per month to your savings, it may grow to as much as $17,565 after 5 years at a 2.3%* annual rate of return.

What you should know about compound interest and your savings accounts

When you open or add money to a savings account, read the rate sheet or account disclosures to determine how frequently interest compounds for your account. You can use a compound interest calculator to estimate how much interest you could earn

Types of accounts that may use compound interest

Compound interest can play a role in how a variety of accounts may help you grow your funds over time. Here’s how it applies in different financial settings:

Savings Accounts

Savings accounts may compound interest daily or monthly. While interest rates may be modest, the compounding frequency can help your savings grow steadily.

Certificates of Deposit (CDs)

CDs may offer higher interest rates than regular savings accounts and compound interest daily or monthly. Because your money is locked in for a fixed term, interest can build up more substantially, especially with longer terms.

Money Market Accounts

Similar to savings accounts, money market accounts may offer tiered interest rates and compound interest daily or monthly, making them an option for those who want a combination of access and earning potential.

Retirement accounts

While some investments like stocks  don’t technically pay compound interest, retirement savings accounts that include CDs or interest-bearing savings instruments may also benefit from compounding.

*Rate provided is for illustrative purposes only.

Disclosure: This article is for general educational purposes. It is not intended to provide financial advice. It also is not intended to completely describe any Citi product or service. You should refer to the terms and conditions financial institutions provide for various products.