Every individual with a monthly gross income that equals or exceeds certain limits is required to file a federal income tax return.

Suppose the progressive table form looks like this:

       gross income               % to be applied
    ----------------------------------------------
    =< 1,000.00                         0%
    > 1,000.00 and =< 1,500.00         10%
    > 1,500.00                         25%
    ----------------------------------------------

Thus:

* If the monthly gross income is US$800.00, the individual pays no tax;

* If it is US$1,200.00, he pays nothing over the first US$1,000.00 plus 10% of US$200.00 (US$1,200.00 - US$1,000.00), a total tax of US$20.00;

* If it is US$1,800.00, he pays nothing over the first US$1,000.00, plus 10% over US$500,00 (US$1,500.00 - US$1,000.00) plus 25% over US$300.00 (US$1,800.00 - US$1,500.00), a total tax of US$125.00.

Write a single math expression, function of those parameters, which gives the value of the tax to be paid.

Are we allowed to use the 'absolute value' function?

If so, here's an idea, first in transparent form:

Tax :=
½(x - 1000 + abs(x - 1000))(10/100) + ½(x - 1500 + abs(x - 1500))(15/100)

which simplifies to

(1/8)x - 325/2 +(1/20)abs(x - 1000)+(3/40)abs(x - 1500)

where x represents the gross salary.

Edited on July 7, 2009, 8:10 pm

Posted by Harry on 2009-07-07 20:09:16