Hi SIMMS7400,
No. That code had not been presented in the mail to which I responded. But we can use it for discussion now. Although the code above happens to work because there is no month zero. Let's look at the tests for the other three quarters:

Code:

if [ $(($(date +%m)/4+1)) -eq 1 ]
... # Happens to work for months 01, 02, and 03
elif [ $(($(date +%m)/4+1)) -eq 2 ]
... # Treats months 04, 05, 06, and 07 as 2nd quarter.
elif [ $(($(date +%m)/4+1)) -eq 3 ]
... # With ksh, treats months 08, 09, 10, and 11 as 3rd quarter.
... # With bash, treats months 08 and 09 as syntax errors and treats months
... #   10 and 11 as 3rd quarter.
elif [ $(($(date +%m)/4+1)) -eq 4 ]
... # With ksh, treats month 12 as 4th quarter.
... # With bash, treats 08 and 09 as syntax errors and treats 12 as 4th quarter.

Everything marked in red in the comments above look wrong to me! Do you believe that October and November should be in 3rd quarter instead of the 4th quarter? Do you believe that July should be in the 2nd quarter instead of the 3rd quarter? What shell are you using? If you're using bash, do you believe that August and September should not be in any quarter in a calendar year?

I believe that Q1 should be months January, February, and March; Q2 should be months April, May, and June; Q3 should be months July, August, and September; and Q3 should be months October, November, and December. That is not what your code does!
Define your terms!
Is FirstQtrWeek supposed to be the 1st Saturday before January 2, of the current year?

Is LastQtrWeek supposed to be the 1st Saturday before XX/02/YYYY where XX is the 1st month of the current quarter in calendar year YYYY?

And, I repeat, what shell are you using?