New York state income tax is based on taxable income which is part of a person\'
ID: 3034495 • Letter: N
Question
New York state income tax is based on taxable income which is part of a person's total income. The tax owed to the state is calculated using taxable income (not total income). In 2005. for a single person with a taxable income between S20.000 and $100.000. the tax owed was S973 plus 6.85% of the taxable income over S20.000. Answer the following questions, and DO NOT include any commas in your final answers. Compute the tax owed by a person whose taxable income is S49.000. Consider a lawyer whose taxable income is 70% of her total income. $x. where x is between S60.000 and S120.000. Write a formula for T(x), the amount of taxable income (not the tax owed, yet). Write a formula for L(x).the amount owed by the lawyer in part (b). Use L(x) to evaluate the tax liability (amount owed) for x = 70,000 and compare your results to part (a).Explanation / Answer
(a) Since 49000- 20000 = 29000 and since 29000*6.85 % = 1986.5, hence tax = $ 973+ 1986.5= $2959.5= $2960 ( on rounding off to the nearest dollar).
(b) The amount of taxable income of a lawyer whose total income is x, is T(x) = x *70 % = $ 0.7 x
(c) The amount owed by the lawyer is L(x) = 973 + 6.85 % of [ T(x) – 20000] = 973 + 0.0685T(x) -1370 = 0.0685T(x) – 397.
(d) If x = $ 70000, then T (x) = 0.7x = 49000 and 0.0685 T(x) = 3356.5. Therefore,the tax owed = 0.0685T(x) – 397 = 3356.5 – 397 = 2959.5 = $ 2960 (on rounding off to the nearest dollar). This is the same amount of tax as in part (a) above. Since the taxable incomes are same ( $ 49000), the taxes have to be same .