Calculating Interest and the Daily Balance method

Posted on February 27, 2011

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I was looking at the American Express High Yield Personal Savings Account and I realized I did not understand the difference between APR and APY. So today I took the time to learn the fundamentals of calculating interest.

First off what does APR and APY represent? APR is the acronym for “Annual Percentage Rate” which is the interest rate for a year without compounding. While APY is the acronym for “Annual Percentage Yield” for the same interest rate but compounded over a year. Even with the same APR, the APY can vary depending on the compounding frequency. The compound rate can happen monthly, weekly, or like the American Express Savings Account, daily.  Most savings accounts, like American Express Personal Savings, uses the Daily Balance Method to calculate the interest daily.

You can calculate the APY from the APR and the compound frequency with the following formula:

APY = (1+r/n)^n - 1

where r is the APR and n is the number of times the balance is compounded in a year.

Formulas are nice and all, but I would like to actually break down how the interest is calculated. Using the daily compound rate as an example, the daily rate is computed by dividing the APR by 365 for 365 days in a year. Then at the end of each day the daily interest rate is used with the current day’s balance to calculate the interest for that day.

That means with interest compounded daily, there is always an incentive to get that check into the savings account as soon as possible. So go deposit those checks you got lying around because you’re losing interest!

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Posted in: Finance