Question

James earns $418 per week and has one exemption. His office’s payroll software is broken and can only compute the withholding for zero exemptions. What weekly salary with 0 exemptions would give the closest exemption to what James should have?

Answer 1

James should earn a weekly salary of $ 432.76 with 0 exemptions to give the closest exemption.

How to estimate the salary without exemption

In this question, we should estimate the salary earned before one exemption and find the equivalent brute salary with no exemptions. The expected salary is equal to product the brute salary minus the product of the tax rate and brute salary.

According to the table we have the expected salary after one exemption:

$x = 418\cdot \left(1-\frac{19.66}{100} \right)$

$x = 335.82$

After a quick inspection to the salary column for zero exemptions, we find that percentage associated to a salary with no exemptions: ($r = 22.40\,\%$)

$C = \frac{335.82}{1-\frac{22.40}{100} }$

$C = 432.76$

James should earn a weekly salary of $ 432.76 with 0 exemptions to give the closest exemption. $\blacksquare$

Remark

The exemption table is missing. The complete figure is shown below.

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