Math Dopers! Need help with pay/leave accrual rate problem

Factual Questions
1

Math Dopers, I need your help. I just can’t wrap my head around this one for some reason!

OK here is the situation:

My boss just changed our leave policy…

**The old system: **

Employees who have been with the company for less than 3 years (henceforth known as “E1”) earn leave at the rate of 8.33 hours per pay period. We get paid twice a month (15th and last day of month) so that means there are 24 pay periods a year.

Employees that have been with the company for more than 3 years (known as “E2”) earn leave at the rate of 9.33 hours per pay period.

So E2 earns 1 more hour of leave per pay period than E1.

The new system:

E1 earns 4.5 minutes of leave per hour.
E2 earns 5.0 minutes of leave per hour.
So E2 earns 0.5 more minutes of leave per hour than E1.

The problem:

I already know that we’re all getting less leave than before. But my question is, before, E2 earned a certain amount more leave per year than E1. How does that amount compare to the new amount? Is E2 still earning the same rate or percentage more leave than E1? Or is the benefit to E2 (the benefit being you get more leave when you have been here longer) lessened with the new arrangement?

The problem I encountered is that I just can’t reconcile the different units (hours per pay period vs. minutes per hour).

Can you help me??

2

Easy. No need to convert the units.

Old system, E2 gets 12% more leave than E1, calculated as ((9.33-8.33)/8.33)*100

New system, E2 gets 11.1% more leave, calculated as ((5-4.5)/4.5)*100

3

Assuming each employee works 40 hours per week, for 50 weeks a year, or 2000 hours per year:

Under the old system, E1 earned 8.33 hours * 24 pay periods = 200 hours of leave per year. E2 earned 9.33 * 24 = 224 hours of leave per year.

Under the new system, E1 earns 4.5 minutes * 2000 = 150 hours per year. E2 gets 5 * 2000 = 167 hours per year.

So E1 gets 50 25% less vacation, and E2 gets about 25% less vacation. So it’s about even.

As Dag Otto mentions (on preview), If all you care about is the relative loss, under the previous arrangement, E2 got (9.33/8.33) = 112% of the vacation E1 got, and under the new system, E2 gets (5/4.5) = 111.1% of the vacation E1 gets. It’s pretty close.

4

THANK YOU! I knew it would end up being a lot more simple than I was making it out to be. Yes that makes sense, and less than 1% difference is no big deal.