You’ve got to make a sales pitch of it. You want them to give you more money for the service you’re already providing. So they need to understand the value of your offer.
Writing is okay, I guess. But I think you’ll find it more satisfying and faster to talk to them in person. If you believe the letter to be helpful, hand deliver it yourself and explain what it is about. This is not email material!
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Were I in your shoes, I would likely attempt starting a conversation – and/or a letter – along these lines:
Thank you for trusting me with the opportunities and responsibilities of my new position as __________________. I’m excited by my new role and am looking forward to the challenge.
With the increased effort, time, and skill needed to fill my new role, I would like to request additional compensation as it’s customary to see an increase in pay with a promotion.
I recommend we sit down at a convenient time together to discuss your thoughts on this. When is a good time for you?
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I realize my wording is a bit formal in places. You’d obviously want to use your own language. However, notice the following aspects of my suggestion:
1. Explain the benefits of your offer. In this case, you’re doing a great job in your new role.
2. Normalize your request. Everyone expects a pay increase with a promotion… but don’t compare your pay to anyone else’s.
3. Make it easy for them. They’re apparently very busy. Ask for what you want, but also be deferential of their time.
4. Make a positive recommendation for the next step. You don’t need a yes/no answer right now. You’re going to give them the illusion of time to think about it. But what you’re really doing is having them plan the time to sit down and talk about how much more they’re going to pay you.
5. Unless you really have a specific amount in mind, don’t give them a dollar/percentage amount for the raise. They know what they paid others in that role… and you’re new. If they ask you to throw out a number, politely tell them you defer to their judgement.
6. Say your piece, then don’t say anything else. Don’t ramble on. Don’t try to fill the awkward silence. As a matter of fact, if there is awkward silence, that’s your cue to stay quiet. Allow them offer something to make the conversation comfortable again.
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Finally, as they say, this is just business. If the pay raise isn’t enough to make you happy, you can tell them that. If they say too bad, don’t get mad. Don’t compare your pay to your friends’. Just do your job professionally – and – starting looking for higher paying jobs elsewhere. You’ve got real career experience now… and it’s valuable somewhere.