Question

Lus

A certain state uses the following progressive
tax rate for calculating individual income tax:
Income Progressive
Range ($) Tax Rate
2%
0 - 2000
2001 - 9000
5%
9001 and up
5.4%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
hole dollar amount

Answer 1

$3,144

Explanation:

Based on your tax table, the tax on an amount x over 9000 will be ...

t(x) = 0.054(x -9000) +0.05(9000 -2000) +0.02(2000)

= 0.054x -9000(0.054 -0.05) -2000(0.05 -0.02)

= 0.054x -36 -60

= 0.054x -96

Then the tax on 60,000 will be

t(60000) = 0.054(60000) -96 = 3240 -96 = 3144

The state income tax owed on $60,000 is $3,144.

_____

Additional comment

The standard calculation can be simplified as shown above. The tax table can be reduced to ...

`t(x)=\begin{cases}0.02x,&x\le2000\\0.05x-60,&20009000\end{cases}`