# How does the APY get applied on a CD that is less than one year?

I know that for interest rates you calculate the monthly rate by dividing by 12 (or similarly for any period by the number of periods/year). But if I have a 3 month CD that has a 0.4% APY, does that mean that I'll see 0.1% (or 0.4*0.25) for the 3 month period?

• Is the 0.4% rate the APR (Annual Percentage Rate) or the APY (Annual Percentage Yield)? What is the compounding period for the interest on this CD? – Ben Miller - Remember Monica May 6 '16 at 18:41
• @BenMiller The 0.4% is APY and first and only payment is at maturity (3 months) – Fueled By Coffee May 6 '16 at 18:49

To clarify. APY will always be an annual number. To calculate your APY you use the formulas below with your APR, the applicable compounding frequency, and duration of an entire year. The more frequent the compounding occurs the greater your yield relative to your rate. When you have a maturity period less than a year, the APY is still calculated based on holding for a full year.

Assuming a 0.4% APR, you will receive 0.4% for the duration of the CD. Generally bank CDs are compounded daily which will help out a bit. You can roughly calculate your return by (assuming a \$1,000 deposit and a 3 month duration):

``````Monthly Compounding: 1000 * ( 1 + .004/12 ) ^ 3

Daily Compounding: 1000 * ( 1 + .004/360 ) ^ 90
``````

On such a short time frame the effects of compounding will be negligible. And the published APY can be largely ignored as you will not be holding the CD for a year, unless you buy another three month CD at the same rate after maturity.

• These two formulas assume either monthly or daily compounding for the APY. Isn't the APY based on annual compounding? – DJohnM May 6 '16 at 19:47
• APY is Annual Percentage Yield. It's very typical for retail banking products to compound daily. While the compounding frequency will affect the yield you're always dealing with an annualized percent. The more frequent the compounding, the greater your yield relative to your rate. – quid May 6 '16 at 19:52
• Banks apply their particular compounding interval to their nominal annual rate to calculate the APY. They do not apply their compounding interval to the APY. – DJohnM May 7 '16 at 5:10
• @DJohnM "The more frequent the compounding, the greater your yield relative to your rate." – quid May 8 '16 at 19:13

According to this Wikipedia article, https://en.wikipedia.org/wiki/Annual_percentage_yield, the Federally defined meaning of APY produces this formula: Assuming a 91-day period for the three month period, we get \$0.9957665 on a \$1000 CD