Question

Concrete Works manufactures and sells cement trucks. For the previous year, their taxable income was $6,775,989.00. They have
to pay a federal tax rate of 35%, a state tax rate of 8%, and a local tax rate of 2%. As part of their loan package for the business, the
company has to pay $3,200,000.00 after the taxes are paid each year to go against the principal amount of the loan. The profit after
taxes and principal reduction can be determined by the equation
p() = 0.586041 - 3,200,000,
where x is their taxable income. How much profit does the company have after paying taxes and reducing the principal on the loan?

Answer 1

You have the right equation.

p(x) = 0.586041x - 3,200,000

3200000 of course represents the deduction from the loan

0.586041 - this number represents the amount of money left after taxes (58.6041% of the total is left)

We get this by taking into account all the taxes on top of another...

35% federal tax = 65% left

35% federal tax and 8% state tax = 65% x 92% left

35% federal tax and 8% state tax and 2% local tax = 65% x 92% x 98% left = 58.6041%

To get the profit plug in the given taxable income for x.

p(6775989) = 0.586041(6775989) - 3,200,000 = $771,007.37 approx.

answer: $771,007.37 approx.