When you take out a loan, you want to pay as little in interest as possible. When you’re opening a deposit account, however, the goal is to earn as much interest as possible. Though these two goals are opposite, understanding how to calculate the effective interest rate when the annual percentage rate compounds daily, sometimes called the annual percentage yield, helps make sure you’re getting the best deal or making the best investment.

#### TL;DR (Too Long; Didn't Read)

When an APR compounds daily, you must take the specific amount of interest earned on a single day and add it back into the principal before calculating interest for the subsequent day. This process repeats throughout the year.

## Significance of Interest Compounding

Each day, interest accrues on a loan or an account based on the amount owed or the account balance. However, not every bank adds the interest to the balance of the account at the end of every day – some do it monthly, quarterly or annually. The more often interest is compounded, the higher the effective interest rate will be because once the interest is added, it begins to accrue additional interest. For example, if interest is compounded daily, the interest accrued on day one starts earning additional interest on day two. If interest is compounded annually, that same accrued interest won’t accrue additional interest until the next year.

As a result, daily interest compounding is beneficial if you’re the one earning interest, such as on a certificate of deposit or savings account. However, if you’re the one paying the interest, such as on a mortgage or credit card, you would save more money if interest weren’t compounded quite as frequently.

## Calculating APY from APR

To calculate the annual percentage yield from the annual percentage rate on an account that compounds interest daily, first divide the annual percentage rate by 365 to calculate the daily interest rate. Second, divide the daily interest rate by 100 to convert it to a decimal. Third, add 1. Fourth, raise the result to the 365^{th} power because there are 365 days per year. You'll need to use the exponent key, often a "^" or "x^y", on your calculator. Fifth, subtract 1 from the result to calculate the annual percentage yield as a decimal. Finally, multiply the annual percentage yield as a decimal by 100 to convert it to a percentage.

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For example, say your savings account pays you an annual percentage rate of 1.46 percent. First, divide 1.46 by 365 to find the daily interest rate equal 0.004 percent. Second, divide 0.004 percent by 100 to convert it to a decimal of 0.00004. Third, add 1 to 0.00004 to get 1.00004. Fourth, raise 1.00004 to the 365^{th} power to get 1.0147. Fifth, subtract 1 to find the annual percentage yield as a decimal equals 0.0147. Finally, multiply 0.0147 by 100 to find the annual percentage yield is 1.47 percent.