Does anybody have an alternate way of solving this problem?
Mann, Inc., has a bonus plan covering all employees. The total bonus is equal to 10% of Mann’s preliminary (prebonus, pretax) income reduced by the income tax (computed on the preliminary income less the bonus itself). Mann’s preliminary income for the year is $200,000 and the income tax rate is 40%. How much is the bonus for the year?
A. $10,800
B. $12,000
C. $12,500
Answer (C) is correct.
The problem requires setting up simultaneous equations because it has two unknowns, the bonus and the tax. Set the tax (T) equal to 40% of income of $200,000 minus the bonus. Set the bonus (B) equal to 10% of the $200,000 income minus taxes. Solve for T and then substitute the resulting value for T in the bonus equation.
T=.4($200,000 – B)
T=$80,000 – .4B
B=.1($200,000 – T)
B=$20,000 – .1($80,000 – .4B)
B=$12,000 + .04B
.96B=$12,000
B=$12,500 bonus
D. $20,000
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