# How Compound Interest Works

Compound interest works by having a loan’s interest rate apply to the principal balance and previously accrued interest. It can work in your favor when you’re saving or investing, or against you if you borrow money.

A loan's interest rate determines how much interest accrues on its principal balance—the original amount. But when interest compounds, interest accumulates on the previously accrued interest and the principal. For savers, that means you can earn interest on your interest. Or, if you're borrowing money, you'll have to pay interest on interest.

## How Does Compound Interest Work?

An example can help make sense of how compound interest can help increase your savings—or debt—over time.

Say you put \$1,000 into a savings account with a 10% interest rate and the interest compounds annually. At the end of the first year, you will have \$1,100. The initial \$1,000 is your principal balance, plus you earn \$100 in interest.

At the end of the second year, you will have \$1,210—the \$1,100 from the previous year, plus \$110 in additional interest (10% of \$1,100). Instead of calculating interest based solely only on your original principal, with compounding interest, the 10% applies to the principal plus accumulated interest.

By the end of the 10th year, you'll have \$2,594, more than double your initial savings—and you can thank compound interest.

The interest on savings accounts typically compounds more frequently than once a year, which could make calculating your returns more difficult. However, to make it simpler, savings accounts advertise an annual percentage yield (APY) rather than an interest rate. The APY includes compounding, and you can use it to determine how much interest you might earn each year.

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## How Is Compound Interest Calculated?

The formula for calculating compound interest is:

A = P(1+r/n)nt

• P is the principal (the starting amount)
• r is the annual interest rate, which is written as a decimal
• n is the number of times the interest compounds each year
• t is the time, or total number of years
• A is the total amount you will wind up with at the end of the timeframe

Fortunately, you don't need to be a math whiz or to calculate interest by hand—there are many online calculators you can plug your numbers into instead. However, the formula can offer insight into compounding.

Whether you're saving or borrowing money, you may already know the amount you'll start with (P) and your timeframe (t). As a result, there are two variables to consider as you compare your options: the interest rate (r) and compounding frequency (n).

The impact of a higher or lower interest rate is fairly straightforward: A higher rate means more interest gets added each cycle.

Similarly, the more often interest compounds, the faster the growth. For example, here's how different frequencies impact the growth of \$1,000 with a 10% interest rate.

Compounding Interest on \$1,000
Compounds Daily Compounds Monthly Compounds Annually
After one year \$1,105 \$1,105 \$1,100
After two years \$1,221 \$1,220 \$1,210
After five years \$1,649 \$1,645 \$1,611
After 10 years \$2,718 \$2,707 \$2,594

## How Does Compound Interest Affect Debt?

While compound interest can help your savings and investments grow faster, it can also work against you when you're borrowing money.

### Compounding Interest and Credit Card Debt

Many credit cards compound interest daily, and you accrue interest based on your average daily balance and a daily periodic rate.

Say your credit card has a \$10,000 balance at the start of your billing cycle. The card has a 25% annual percentage rate (APR), and its daily periodic rate is 0.25 / 365 = .00068. (Some card issuers use 360 days instead of 365.)

Here's how the interest compounds and accumulates if you don't make any new purchases or payments.

• You have a \$10,000 balance on the first day.
• On the second day, the card issuer calculates your daily balance by adding new transactions to the previous day's balance, including accrued interest: \$10,000 x .00068 = \$6.85 in interest, so your new balance is \$10,006.85.
• This repeats the next day: \$10,006.85 x .00068 = \$6.85, and your new balance is \$10,013.70.
• The daily interest amount increases by the third day: \$10,013.70 x .00068 = \$6.86, and your new balance is \$10,020.56.

Although this is basically what's happening behind the scenes, you won't see the interest charges added to your credit card's balance throughout the month if you log in to your account each day.

Instead, credit card issuers may divide the sum of your daily balances by the number of days in the billing cycle to find your average daily balance. They multiply that by your daily periodic rate, and multiply the product by the number of days in the billing cycle.

And although the compounding doesn't lead to a large increase in interest charges from one day to the next, it's one reason paying off credit card debt can be difficult. Continuing the example above, by the end of a 30-day billing cycle, your balance will be \$10,186.59.

### Compounding Interest on Other Types of Debt

Other types of loans might use a different compounding schedule, such as monthly or annually. When interest compounds less frequently, you may be able to avoid compounding interest by paying all the accrued interest before the start of a new compounding period. For example, if the interest compounds monthly, try to pay at least all the accrued interest each month.

Additionally, some loans use simple interest instead of compound interest, meaning the interest rate only applies to the principal balance. Although the interest doesn't compound, if your monthly payment doesn't cover the monthly interest, then your overall loan balance grows—what's known as negative amortization. In some cases, that unpaid interest might get added to your principal balance. Then, the interest rate may apply to the new, larger principal balance.

When you're applying for any type of loan, but especially a large loan, make sure you understand how interest accumulates and when it compounds.

## How to Avoid Compound Interest on Credit Cards

High interest rates and daily compounding can make credit card debt relatively expensive, but there are ways to use credit cards without paying interest:

• Pay your balance in full. Credit cards often have a grace period, and your purchases won't accrue interest if you pay your statement balance in full each month.
• Use an introductory 0% APR offer. Some credit cards have intro 0% APR offers, giving new cardholders a 0% APR during a limited promotional period. You can use the promotional rate to avoid accruing interest on your purchases, even if you carry a balance, but try to have a plan for paying off the balance in full before the promotional period ends.
• Transfer a balance. Similarly, balance transfer credit cards offer a promotional 0% APR rate on balances that you transfer to the card. You can transfer credit card debt that's currently accruing interest to one of these cards and then pay down the balance while it's not accruing interest. However, read the fine print, as interest may still accrue and compound on new purchases.

If you can't avoid credit card interest altogether, you can also look into different ways to lower your credit card's interest rate.

## Improve Your Credit to Save When Borrowing

Your credit score doesn't affect whether a loan uses compound interest or the compounding frequency. However, good credit can help you qualify for a lower interest rate on credit cards and loans. Check your credit report and credit score from Experian for free, and get tips on how to improve your credit score.