I am a student and have been working part-time in a company. I have never received an increase in my hourly rate, but I received an email from CEO saying that they give me a bonus of $500 from the manager, should I respond to the email by saying thank you? How should I respond to the email? What is the etiquette?
We gave our people bonuses pretty regularly. The first time, we might tell them in person or an email. (With long term employees who knew there was generally a financial year end bonus and a calendar year end bonus I might not mention it.) Generally, they said thankyou, and I was never offended by anybody thanking me for a bonus. On the other hand, if they just said "cool!" or "great!" in person without the magic words "Thank you" or if they didn't reply to the email, I didn't hold that against them. Of course, you might work for someone who is a little more petty or in need of validation, who would hold it against you that you didn't thank them.
You can't go wrong with a simple thankyou email. Don't tell them how desperately you needed the money or anything like that, and don't overshare in general. Something like "Thanks, I'll put that to great use" is more than enough. If you want, you could also include a sentence that indicates you understand bonuses mean the company is doing well, and you're happy the company is doing well.
It might depend on how large your company is.
For a small company this likely isn't an issue and will be welcome. However for a large company while it won't get you in trouble it may be unnecessary or unwelcome.
Think about a few things; 1) have you met the CEO, 2) have you had a meaningful interaction with the CEO, 3) would the CEO know you by name if bumped into them at the office, 4) how many employees does company have, and 5) how many employees receive bonuses?
If your answer to first three of these is "No" and the answer to the last two is "a lot", then you may be basically sending your CEO a spam message. If the company has hundreds of employees and many are sending the CEO "thanks" messages it will clog up their inbox and cause frustration. Just like on SE we avoid thank you comments, answers, and for the most part saluatories in posts. It can become overwhelming to have to sort through all that, even if they go straight to the trash folder.
If your answer to first three of these is "Yes" and the answer to the last two is "not many", then the email will probably be appreciated. However, it may also be better just to thank them in person as well.
You also mention that the bonus is "from the manager". In that case it would be a better option to thank the manager as they are likely responsible for you receiving the bonus. Larger companies tend to have a certain budget for bonus types that managers submit for. While the CEO likes to send out the company wide email, they may not have had a real hand in you getting the bonus. Sending the email to your manager will also let them know you did in fact receive or were approved for the bonus they submitted for you.
In all cases where you do send the email, keep it short and positive.
I would say more than a one line "thank you" but not more than two or three sentences. Something along the lines of "Thank you, Mr. CEO. I appreciate the recognition and look forward to another productive year."