perplexus.info :: Just Math : Payroll

Payroll (Posted on 2005-01-02)

The ABC Widget company paid its salaried employees each month 1/12 of their annual rate of pay. Then, on a month that began on a Sunday, they switched to paying them every other week 1/26 of their annual pay.

Alice said that works out worse for the employees, as in the first month, they'd get only 1/13 of their annual pay instead of 1/12.

Bob said "No, you're getting some of your money sooner by two weeks, more than making up for it, so that it's better for the employees."

Who is right?

Submitted by Charlie

Rating: 3.7500 (4 votes)

Solution: (Hide)

Taking interest at 1% annual rate, the following table shows the amount received up to that point, together with the interest it would earn (or avoid if borrowed), at the end of each of the first twelve months of monthly pay for someone making $100,000 per year:

8333.33 16673.61 25020.84 33375.02 41736.17 50104.28 58479.37 66861.44 75250.49 83646.53 92049.57 100459.61

After each of the first 26 two-week pay periods:

3846.15 7693.76 11542.83 15393.36 19245.34 23098.79 26953.69 30810.05 34667.88 38527.16 42387.91 46250.12 50113.79 53978.93 57845.53 61713.60 65583.13 69454.12 73326.58 77200.51 81075.91 84952.77 88831.11 92710.91 96592.18 100474.92

So the advance by over two weeks of almost half the monthly pay more than compensates for the delay in part of the first month's pay into the next month.
Plus, that's for only 364 days. Bumping up by 365.25/364, the overall effective rate plus interest is now 100819.96.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Not of interest	Steve Herman	2006-05-29 13:50:08
re: This is of interest...	Larry	2005-01-03 13:52:57
This is of interest...	Penny	2005-01-03 11:33:37
My Answer	Thomas Chen	2005-01-03 07:45:32
re(2): Solution	Penny	2005-01-02 20:46:48
re: Solution	Penny	2005-01-02 19:18:20
Salaried employees	Larry	2005-01-02 19:02:24
It Depends	Larry	2005-01-02 18:34:34
Solution	Penny	2005-01-02 17:33:14
Guess	sassy	2005-01-02 17:30:08

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info