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

Answer 2

The bonus for the year would be $12,500 when Mann, inc. Has a bonus plan covering all employees.

What is the bonus?

Bonus is usually paid to the employees by their employers in addition to their actual salary.

Bonuses may be allocated by a company as an inducement or to reward great performance.

Computation of the bonus:

According to the question,

Bonus :

$\text{Bonus} = \text{Bounus Percentage} \times\ (\text{Preliminary Income}- \text{Taxes})\\\\\text{Bonus} = 10\% \times (\ 200,000 - \text{taxes})\\\\\text{Bonus} = \ 20,000 - 0.1\times\rm{Taxes}$

Now, we have to find the value of taxes:

$\rm{Taxes} = \text{Tax Rate}\times\text{Preliminary Income- Bonus}\\\\\rm{Taxes} = 40\% x (\ 200,000 - \text{Bonus})\\\\\rm{Taxes} = \ 80,000 - 0.4\timesitext{Bonus}$

Now, by arranging the above two equations, we get:

$\text{Bonus} = \ 20,000 - 0.1\times(\ 80,000 - 0.4\times\rm{Bonus})\\\\\text{Bonus} = \ 20,000 - \ 8,000 + 0.04\times\text{Bonus}\\\\Bonus - 0.04\times Bonus = \ 12,000\\\\0.96\times Bonus = \ 12,000\\\\Bonus = \dfrac{\ 12,000}{0.96}\\\\ Bonus= \ 12,500$

Therefore, the bonus amount for the year would be $12,500.

To learn more about the bonus, refer to:

https://brainly.com/question/19067255