Determining Formula Given Accrual Schedule

Good morning. Our company has long lost the formula behind determining how paid time off is calculated. I need to determine it now b/c we have added a level to the accrual schedule (over 25 years).

Immediately (5 paid days off)

1 calendar month completed = 0 days
2 calendar months completed = 1
3 calendar months completed = 1
4 calendar months completed = 1 1/2
5 calendar months completed = 2
6 calendar months completed = 2 1/2
7 calendar months completed = 3
8 calendar months completed = 3
9 calendar months completed = 4
10 calendar months completed = 4
11 calendar months completed = 4 1/2
12 calendar months completed = 5

1 year of service through 7 years (15 days)

1 calendar month completed = 1
2 calendar months completed = 2 1/2
3 calendar months completed = 3 1/2
4 calendar months completed = 4 1/2
5 calendar months completed = 6
6 calendar months completed = 7 1/2
7 calendar months completed = 9
8 calendar months completed = 9 1/2
9 calendar months completed = 11 1/2
10 calendar months completed = 12
11 calendar months completed = 13 1/2
12 calendar months completed = 15

8 -15 calendar years (20 days)

1 calendar month completed = 1
2 calendar months completed = 3 1/2
3 calendar months completed = 5
4 calendar months completed = 6 1/2
5 calendar months completed = 8
6 calendar months completed = 9
7 calendar months completed = 12
8 calendar months completed = 13
9 calendar months completed = 15
10 calendar months completed = 16 1/2
11 calendar months completed = 18 1/2
12 calnedar months completed = 20

16-25 calendar years (25 days)

1 calendar month completed = 1 1/2
2 calendar months completed = 4
3 calendar months completed = 6
4 calendar months completed = 8
5 calendar months completed = 10
6 calendar months completed = 12 1/2
7 calendar months completed = 14 1/2
8 calendar months completed = 16
9 calendar months completed = 19
10 calendar months completed = 20 1/2
11 calendar months completed = 22 1/2
12 calendar months completed = 25

Hopefully this makes sense. I apologize for the length of the question and if I have put it in the wrong section.

Any help determining the formula and the next schedule (30 paid days off) is greatly appreciated!

16-25 calendar years (25 days)

1 calendar month completed = 1 1/2
2 calendar months completed = 4
3 calendar months completed = 6
4 calendar months completed = 8
5 calendar months completed = 10
6 calendar months completed = 12 1/2
7 calendar months completed = 14 1/2
8 calendar months completed = 16
9 calendar months completed = 19
10 calendar months completed = 20 1/2
11 calendar months completed = 22 1/2
12 calendar months completed = 25

Click to expand...

There is no complex formula involved here. Examination of the 25 day allocation pretty much follows the pattern of dividing 25 by 12, then multiplying by the number of months completed. The results were then rounded “down” for the most part.

However, when allocating 30 days, no rounding is required since allocations are given to the nearest half day. You might consider an allocation such as the following, which allocates 2.5 days each month:

More than 25 calendar years (30 days)

1 calendar month completed = 2 1/2
2 calendar months completed = 5
3 calendar months completed = 7 1/2
4 calendar months completed = 10
5 calendar months completed = 12 1/2
6 calendar months completed = 15
7 calendar months completed = 17 1/2
8 calendar months completed = 20
9 calendar months completed = 22 1/2
10 calendar months completed = 25
11 calendar months completed = 27 1/2
12 calendar months completed = 30

Hope that helps.

Thank you for the reply wjm11. I also tested the (N/12) * M formula, with N being the number of paid days off and M the number of months completed. I tried both rounding down and rounding to the nearest 1/2 day, neither of which gave me answers entirely consistent with those already in place.

You mention that "when allocating 30 days, no rounding is required since allocations are given to the nearest half day." I'm not sure I follow you there since the answers vary depending on the rounding method you use.

I don't really want to break from the previous pattern and allocate 2.5 days per month, so how would you suggest I allocate the days otherwise for the over 25 year schedule?

Thanks again for you time.

As you noted, the (N/12) * M formula was only approximated in past allocations, and the rounding was inconsistent. However, that formula can be used *exactly* to allocate the 30 days without any rounding. The result would be as I already posted (2.5 days per month). I do not have an alternative schedule to offer.

Ok, I'm following you now. Thank you!