Question

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?

Answer 1

Answer:

$12,500

Explanation:

Bonus = 10% x ($200,000 - taxes)

Bonus = $20,000 - 0.1T

So we must now find T:

T = 40% x ($200,000 - Bonus)

T = $80,000 - 0.4Bonus

now we can replace:

Bonus = $20,000 - 0.1($80,000 - 0.4Bonus)

Bonus = $20,000 - $8,000 + 0.04Bonus

Bonus - 0.04Bonus = $12,000

0.96Bonus = $12,000

Bonus = $12,000 / 0.96 = $12,500