Payroll Tax reimbursement calculation

AskGenie

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Mar 3, 2015
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Hello there,

I work with a union contractor that is required to pay the employee portion of his social security. Easy right, 7.65 of gross. The problem here is that the gross pay changes once you add back in the social security tax. by manual trial and error i came up with a factor of 8.261. I don't even know where to begin to arrive at that number with a mathematical expression. Can someone help please?

Jeannie
 
Hello there,

I work with a union contractor that is required to pay the employee portion of his social security. Easy right, 7.65 of gross. The problem here is that the gross pay changes once you add back in the social security tax. by manual trial and error i came up with a factor of 8.261. I don't even know where to begin to arrive at that number with a mathematical expression. Can someone help please?

Jeannie

As far as I know, gross pay does not include tax paid by the employer.
 
As far as I know, gross pay does not include tax paid by the employer.

This is not tax paid by the employer (employer portion). The employer is reimbursing the employee their portion of the tax. This reimbursement is a cash union benefit so the IRS considers this taxable income subject to more taxes. This is why i need to somehow gross up the tax percent so that on the check stub the amount deducted is equal to the amount paid to the employee. By trial and error i grossed up 7.65 to 8.26 percent. Grossing up the tax percent makes it so the deduction amount is equal to the reimbursement amount. This is the right percent number but I'm in need of a mathematical formula to come up with the 8.26.
 
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This is not tax paid by the employer (employer portion). The employer is reimbursing the employee their portion of the tax. This reimbursement is a cash union benefit so the IRS considers this taxable income subject to more taxes. This is why i need to somehow gross up the tax percent so that on the check stub the amount deducted is equal to the amount paid to the employee. By trial and error i grossed up 7.65 to 8.26 percent. Grossing up the tax percent makes it so the deduction amount is equal to the reimbursement amount. This is the right percent number but I'm in need of a mathematical formula to come up with the 8.26.

I got it!

Let:

SS tax rate = T = 0.0765

Total pay = P

Grossed up additional pay to compensate for tax = x * P

Then

T * (P + x * P) = x * P

T + x * T = x

x*(1 - T) = T

x = T/(1- T) = 0.0765/(1-0.0765) = 0.082837 = 8.2837% (fixed it ...)
 
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