How to find the corresponding APR to a given APY? Suppose that ​$6000 is invested in a 3​-month CD with an APY of 1.5​%
I want to find the corresponding APR to a given APY. If 6000$ is invested in a 3​ month CD with an APY of 1.5​% then according to my calculations, the corresponding APR is 1.491%
I used this relation between APY and APR to get this result: $$APY=(1+ \frac{APR}{n})^{n} -1$$
Where $n$ denotes the $n$ compounding periods per year, I'm not sure what value $n$ should take, but in my case, I guessed that $n=4$ (based on the 3 months CD). So according to this formula by writing the APY in decimal point I got the result that the APR is 1.491% but I'm not really sure if that's tru.
The length of the CD is not relevant. The point of APR and APY numbers is that they annualize the rate you pay over a time frame that may be smaller or larger than a year. What matters is the compounding frequency. CDs generally compound on either a daily or monthly basis, so n will be 12 or 365, depending on the CD.
Is this a real-life problem or an homework/practice question? If it's the latter, you should probably assume n=12 because teachers seldom want you to mess with daily compounding without also telling you how many days you should assume there are in a year for compounding purposes.