<p>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 <em>frequency</em>. CDs generally compound on either a daily or monthly basis, so n will be 12 or 365, depending on the CD.</p>
<p>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.</p>

CC BY-SA 4.0
2020-07-08T05:50:07.640Z
2020-07-08T05:50:07.640Z
farnsy
<p>Suppose that ​$6000 is invested in a 3​-month CD with an APY of 1.5​%</p>
<p>I want to find the corresponding APR to a given APY. If 6000$ is invested in a 3​ month CD with an APY of 1.5​% then according to my calculations, the corresponding APR is 1.491%</p>
<p>I used this relation between APY and APR to get this result: <span class="math-container">$$APY=(1+ \frac{APR}{n})^{n} -1$$</span>
Where <span class="math-container">$n$</span> denotes the <span class="math-container">$n$</span> compounding periods per year, I'm not sure what value <span class="math-container">$n$</span> should take, but in my case, I guessed that <span class="math-container">$n=4$</span> (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.</p>

<interest-rate>
How to find the corresponding APR to a given APY?
user144435
# How to find the corresponding APR to a given APY?

(Asked by: username_0 on 2020-07-07)

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.

**Tags:** interest-rate

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## 1 answers

### Answer by username_1 on 2020-07-08. Score: 1

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.


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