Calculating proration

Okay, so, my issue is that I don't know how to do the math to calculate a proration where the proration is over 100%.

Basically, let's say someone is getting a 3% raise.

They're making 100k, 3% is 3k, so their new salary is 103k

I can come up with an excel formula for that.

But if they're prorated at, let's say, 115.89%, what do I do in that case? I feel like I'm missing something rather obvious.

Prorate means to allocate one number proportionally to another. For example, let's say your monthly rent for an apartment is $900 (not in NoVa , but work with me here). You move in on the 21st of the month so you live there for 10 days. They prorate the rent based on a 30-day month, so you pay 10/30 * $900 = $300 for the first month.

I don't know what you mean when you talk about prorating a salary.

Sorry - it's the same, only for a year's worth of work (365 days).

They prorate the rent based on a 30-day month, so you pay 10/30 * $900 = $300 for the first month.

Yes, however the difference is instead of moving in on the 21st, you move in the prior month, on some other day - say the 21st. So, it would be 30 day + the 9 for the previous month. Which is odd, yes. With where I'm working, we have a cut off. So, you get hired on a certain month, you aren't considered for the merit. Cut off is, example, July 1st, the merit is October. You get hired on July 2nd, you wouldn't get a prorated merit, but next year you would get the full 100% plus the difference between July 2 and October.

Does that make sense?

That in mind, person is making 100k
They're getting a 3% increase.
Normally that would be 103k, but I have to figure in the proration (which isn't cutting the amount, but adding to it).

Am I making sense?

Okay, thank you - I believe that works. It was throwing me what to do.

That answers your question but I am still confused about your real-world process. I have never heard of prorating a salary at more than 100%. The Excel answer to this is easy but I want to make sure you are following the right business process.

Yeah, I know, I've never heard of it either. I haven't been fully informed on the reason - I did hear that one of the reasons was because the merit cycle went for a month +.

When we gave people raises, it was always for the upcoming calendar or fiscal year. We never prorated anything when giving raises. We applied the raise, then -bang- that's your new annual salary.

I've worked at places that will prorate your merit/raise or what have you, but not the way I'm currently doing it. I think that's why it broke my brain trying to think of how to do it. I have checked prior years work, btw, so I know this is a historical thing. I'm just not entirely sure why.

If 100k is a pro-rated salary at 115.89%, then the actual salary should be 100k/115.89%=86,288.72.
So, the new salary after 3% raise should be: 100,000/115.89%*(1+3%)=88,877.38.

Pro-rate at over 100% could be due to previous year salary paid this year, e.g. 5 days work in the starting employment month (last month of salary year) added to the next month (first month of following salary year).