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 $20,000 and $100,000, the tax owed was $973 plus 6.85% of the taxable income over $20,000. Answer the following questions, and DO NOT include any commas in your final answers.
(a) Compute the tax owed by a person whose taxable income is $81,000.
tax = $ (round to nearest dollar)
(b) Consider a lawyer whose taxable income is 90% of her total income, $x, where x is between $60,000 and $120,000. Write a formula for T(x), the amount of taxable income (not the tax owed, yet).
T(x) =
(c) Write a formula for L(x), the amount owed by the lawyer in part (b).
L(x) =
(d) Use L(x) to evaluate the tax liability (amount owed) for x = 90 ,000 and compare your results to part (a).
L( 90000 ) = $ (round to nearest dollar)
a) 973 + .0685 ( 81000 - 20000)
b) T = .9 x
c) L = 973 + .0685 (.9 x - 20000)
d) 973 + .0685 (.9*90000 - 20000) same as a above
(a) The tax owed for a person with a taxable income of $81,000 can be calculated as follows:
Tax owed = $973 + 6.85% of (taxable income - $20,000)
= $973 + 6.85% of ($81,000 - $20,000)
= $973 + 6.85% of $61,000
= $973 + $4,186.50
= $5,159.50
So, the tax owed by a person with a taxable income of $81,000 is $5,159 (rounded to the nearest dollar).
(a) Tax owed = $5,159
(b) Since the lawyer's taxable income is 90% of her total income x, we can calculate the taxable income using the formula:
T(x) = 0.9x
(c) To find the amount owed by the lawyer (L(x)), we'll use the formula:
L(x) = $973 + 6.85% of (T(x) - $20,000)
= $973 + 6.85% of (0.9x - $20,000)
(d) To evaluate the tax liability for x = $90,000, we substitute the value into the L(x) formula:
L(90,000) = $973 + 6.85% of (0.9(90,000) - $20,000)
= $973 + 0.0685(81,000 - $20,000)
= $973 + 0.0685(61,000)
= $973 + $4,177.85
= $5,150.85
The tax liability for x = $90,000 using the L(x) formula is $5,151 (rounded to the nearest dollar). This is slightly different from the previous answer in part (a) due to rounding and the slight difference in calculations.
(a) To compute the tax owed by a person whose taxable income is $81,000:
Tax owed = $973 + (6.85% of taxable income over $20,000)
Taxable income over $20,000 = $81,000 - $20,000 = $61,000
Tax owed = $973 + (6.85% of $61,000)
Tax owed = $973 + (0.0685 * $61,000)
Tax owed = $973 + $4,188.50
Tax owed = $5,161.50
Therefore, the tax owed by a person with a taxable income of $81,000 is $5,161.50.
(b) Since the lawyer's taxable income is 90% of her total income, we can write the formula for T(x) as:
T(x) = 0.9x
This formula represents the amount of taxable income (not the tax owed) for a lawyer with a total income of x.
(c) To calculate the amount owed by the lawyer in part (b), we can use the previously derived formula for T(x) and calculate the tax owed using the same method as in part (a):
L(x) = $973 + (6.85% of T(x) - $20,000)
L(x) = $973 + (6.85% of (0.9x - $20,000))
L(x) = $973 + (0.0685 * (0.9x - $20,000))
Simplifying the formula gives:
L(x) = $973 + (0.06165x - $1,373)
L(x) = 0.06165x + $973 - $1,373
L(x) = 0.06165x - $400
Therefore, the formula for the amount owed by the lawyer in terms of her total income x is L(x) = 0.06165x - $400.
(d) To evaluate the tax liability (amount owed) for x = $90,000, we can substitute x = $90,000 into the formula for L(x):
L($90,000) = 0.06165 * $90,000 - $400
L($90,000) = $5,529 - $400
L($90,000) = $5,129
The tax liability (amount owed) for an income of $90,000 is $5,129.
Comparing this result to part (a), we see that the tax liability is different for different income levels.
(a) To compute the tax owed by a person with a taxable income of $81,000, we need to find the amount over $20,000 and apply the tax rate of 6.85%.
First, determine the excess taxable income over $20,000:
Excess taxable income = $81,000 - $20,000 = $61,000
Next, calculate the tax owed:
Tax owed = $973 + 6.85% * (excess taxable income)
Tax owed = $973 + 0.0685 * $61,000
Tax owed = $973 + $4,185.50
Tax owed = $5,158.50
Therefore, the tax owed by a person with a taxable income of $81,000 is $5,158 (rounded to the nearest dollar).
(b) If the lawyer's taxable income is 90% of her total income (x), the formula for T(x), the amount of taxable income, can be written as:
T(x) = 0.90 * x
(c) To calculate the amount owed by the lawyer in part (b), we can use the formula for taxable income (T(x)) in conjunction with the tax calculation formula mentioned in the problem.
The tax owed is calculated as:
L(x) = $973 + 6.85% * (T(x) - $20,000)
Substituting the formula for T(x) into L(x), we get:
L(x) = $973 + 6.85% * (0.90 * x - $20,000)
(d) To evaluate the tax liability for x = 90,000, substitute the value into the formula for L(x):
L(90,000) = $973 + 6.85% * (0.90 * 90,000 - $20,000)
L(90,000) = $973 + 6.85% * (81,000 - $20,000)
L(90,000) = $973 + 0.0685 * 61,000
L(90,000) = $973 + $4,185.50
L(90,000) = $5,158.50
The tax liability for x = $90,000 is $5,158 (rounded to the nearest dollar), which matches the result from part (a).