Banks sometimes perform daily compounding of bank accounts and investment instruments like certificates of deposit (CD). The benefit of daily compounding is to avoid the problem of how to calculate interest for partial periods, for example if a withdrawal is made in between quarterly compounding dates. When banks determine the daily interest rate from the annual rate, they use either a 365-day year or a 360-day year. The 360-day year is more common because of its historical adoption before computers. It affords division of the calendar into 12 30-day months, making pre-computer hand calculations easier. If the bank is paying out, as in the case of a bank account, the 360 method counts 30 days per month per year, including February. If the bank is collecting, as in a mortgage, it collects daily, earning it an extra 5 days of interest.

- Skill level:
- Moderately Easy

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### Things you need

- Calculator with an exponent key

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## Instructions

- 1
Divide the nominal, or stated, interest rate by 360 or 365, depending on whether you picked the "360 over 360" method or the "365 over 365" method. Denote the result with a letter d, for the daily rate.

- 2
Add 1 and raise it to an exponent with the number of days you want to compound the bank account. Use 30 days per month if the bank is the one making payments. This is called the 30/360 method, or "bond basis."

For example, if you want to compound a daily rate of 6%/360 from January 28 to March 1, you'd count 2 days for January, 30 for February, and 1 for March. The 30/360 method means you compound 30 days per month. You'd therefore multiply the principal by (1 + 6%/360)^33 = 1.00551. (The claret "^" denotes the exponentiation.)

- 3
Determine the daily rate from the annual effective rate by finding the 365-th root. Note that by "effective rate" does not mean the APR, which includes escrow payments and other charges in addition to interest.

For example, if the effective rate is 6%, the daily rate is 1.06^(1/365) - 1 = 0.0160%.

#### Tips and warnings

- If you're calculating daily mortgage interest using a 360-day year, you'd use what's called the "Actual/360" method. You'd divide the interest by 360, then exponentiate to 365 to get the total for the year. Needless to say, this makes the bank more interest for the same nominal rate than if they'd used the 30/360 method.