Income tax in a particular country is calculated according t

Income tax in a particular country is calculated according to the following rate schedule: 10% on the first $9,000 of income 18% on the next $26,000 of income 29% on any further income a. How much income tax should be paid by someone making $31,300? b. How much income tax should be paid by someone making $71,900? c. Construct a piecewise function that gives the tax for $x of income.

Solution

Let $x be the income and assume x

10% on the first $9,000 of income = 0.1*9000 = $ 900

18% on the next $26,000 of income = 0.18*26000 = $4680

29% on further income = (x -26000 - 9000)*0.29 = 0.29x -10150

c) So, piece wise function:

f(x) = 0.1x for x<= 9000

= (x -9000)0.18

= 0.18x -1620 for 9000 < x<=26000

= 0.29x -10150 for x > 26000

a) Income = 31300

Tax = 0.1*9000 + (31300 - 9000)0.18 = $ 4914

b) Income = $ 71900

Tax = 0.1*9000 + (26000)0.18 + 36900*0.29 = 900 +4680 +10701 = $ 16281