## What Is Compound Interest?

Compounding interest earns interest on both your initial investment and the money that investment earns.

When investing a sum of money, you’ll earn interest on the initial balance – as well as on the earned interest. To allow greater growth on your initial investment, it’s important to keep your money deposited in the bank over the long-term.

## The Compound Interest Formula

The formula for compound interest is as follows:

A = P (1 + r n ) nt

• P = initial principal (e.g. your deposit, initial balance, “current amount saved”)

• r = interest rate offered by the savings account

• n = number of times the money is compounded per year (e.g. annually, monthly)

• t = number of time periods elapsed/how long you plan to save

• A = final amount, including the initial principal and all interest earned over n years

You can use this formula for your calculations – or use our compound interest calculator above.

## How to Use This Compound Interest Calculator

Before calculating compound interest, let’s break down this financial calculator’s components:

### Initial Balance

The amount of money you begin your account with is called the initial balance. For example, if you opened your investment account with \$500, your initial balance would be \$500.

### Rate of Return (Interest Rate)

Rate of return is the percentage earned on your investment. For example, if you earn a 4% APY on your account, your rate of return is 4%.

### Time Period

A time period is the length of time that money will be kept in your account. The longer the time period, the more your money will compound.

### Regular Contributions

Determine how much money you’ll be contributing regularly (e.g. weekly, monthly). The dollar amount is important, so it’s best to stay consistent with your contributions for the best outcome, like contributing \$100 every month. This is also referred to as dollar-cost averaging.

### Frequency of Compounding

Compounding frequency is what makes your savings or investments grow. Daily compounding is the most impactful because you’ll earn interest each day, but most banks and financial institutions offer monthly and yearly compounding. While each option is favorable, your earnings will grow slower with less frequent compounding.

## Example of Compound Interest

Say that you invest \$250 at a 5% interest rate that’s compounded yearly. In the first year, you’d earn \$12.50 in interest, making your new balance at the end of the year \$262.50.

If you leave that \$262.50 in the account for another 3 years, the new balances (including acquired interest) compound, and you’ll earn the following:

• Year 2 - \$13.13 in interest for a balance of \$275.63

• Year 3 - \$13.78 in interest for a balance of \$289.41

As you can see, the interest added to the principal balance continually compounds or grows, allowing your earnings to earn even more money.

## Complex Compound Interest Example

Take a look at a monthly compounding example so you can see the difference:

You invest the same \$250 at a 5% interest rate that’s compounded monthly. Within the first month, you’d earn \$1.04 in interest, bringing your balance to \$251.04.

If you leave that \$251.04 in the account for an additional 11 months, the new balances would compound each month:

• Month 2 - \$1.04 for a balance of \$251.04

• Month 3 - \$1.05 for a balance of \$252.09

• Month 4 - \$1.05 for a balance of \$253.14

• Month 5 - \$1.05 for a balance of \$254.19

• Month 6 - \$1.06 for a balance of \$255.25

• Month 7 - \$1.06 for a balance of \$256.31

• Month 8 - \$1.07 for a balance of \$257.38

• Month 9 - \$1.07 for a balance of \$258.45

• Month 10 - \$1.08 for a balance of \$259.53

• Month 11 - \$1.08 for a balance of \$260.61

• Month 12 - \$1.09 for a balance of \$261.70

You can compare the balances after one year of yearly compounding and monthly compounding accounts. Although you initially invested the same amount, in the first year, the monthly compounding account earned \$0.80 less in interest than the yearly compounding account.

## How to Make Compounding Interest Work for You

Even if you start with a small sum, compounding interest is the ideal way to save for retirement, emergencies, college, and other large expenses. The earlier you start saving or investing, the faster your money will grow.

But just like earning interest on the interest from your savings or investment accounts, you’ll pay interest on your interest for consumer debts (e.g. credit cards).

Most credit cards use daily compounding interest, meaning they add the interest to your balance and you’re charged interest on the higher balance (your principal plus the interest) the next day. The interest continually compounds until the bill is paid off in full.

## Let Compound Interest Work for You

Whether you’re saving for retirement, a mortgage, or a rainy day fund, the more often you contribute to your account – and the more frequent the compounding – the faster you’ll reach your financial goals.