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Interest rate and annual percentage yield (APY) are two different things, though they are related terms. When you open a savings account, you’ll often be given both numbers, usually expressed in percentages. The bank will typically emphasize the APY over the interest rate. It is often a higher percentage, which means the account yields greater interest than the interest rate.
Arriving at interest rate is a very simple equation. Say a bank offers a 10% yearly interest on a savings account. If you plop $1000 US Dollars (USD) into a bank account at the beginning of the year, then common sense and easy math would dictate you’d have $1100 USD at the end of the year. This is only accurate if the interest is not compounded during the year. However, in most cases, interest is compounded on a weekly, daily or monthly basis. When interest is compounded more frequently, annual percentage yield is a higher percentage.
For example, if your interest is compounded monthly, each month, you’d have one-twelfth of 10% added to your total account or roughly .83% interest added. In the first month, you’d make $8.30 USD. The next month, when your interest is compounded again, you’d have $1008.30 to which the monthly rate would be applied. So you would add about $8.34 to your total balance. The more often interest in compounded, the higher the APY becomes as the year advances. Provided you left your money untouched for a year, by the end of the year, APY would be 10.471%, and you’d have $1104.71. If interest was compounded daily, the APY would be 10.516%.
The formula to calculate APY is based on interest rate and the number of times per year interest in compounded. The following formula is applied, where x = number of times interest is compounded and r = quoted interest rate:
(1 + r ÷ x)x – 1
In language terms, APY is 1 plus the interest rate divided by the number of times interest is compounded yearly, and raised to the number of times interest is compounded yearly. This total then has 1 subtracted from it, to derive the APY. It’s a complicated formula and there are a number of APY calculators online if you don’t have access to a scientific calculator.
To get the best deals on your investments, look for APY rates that are higher than interest rates. Remember that frequency of compounding interest will raise the rates. When possible you want to find accounts that compound daily because these produce the highest yield. Also bear in mind that the APY gets complicated if you withdraw money from your account. APY rates presume that you’ll let the money sit for a year’s time without touching it. If you lower your savings account balance, you’ll lower your earnings for the year.
Your first guess is the correct one. For clarification, read the paragraph that begins "In language terms..." A rule of thumb is that when the order of operations is unclear, do them in this order *, /, +, -. As a child, I learned them as "My dear aunt Suzy."
Is that formula (1 + (r/x))^x - 1, or rather ((1 + r)/x)^x - 1?
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