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QuestionCalculate the state income tax for a salary of \$60,000 using the given progressive tax rates. Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The salary is 60,000peryear..Thetaxratesareappliedprogressively,meaningthattherateforeachincomerangeappliesonlytotheincomewithinthatrange.<br/>3.Theincomerangesandtaxratesareasfollows−60,000 per year. . The tax rates are applied progressively, meaning that the rate for each income range applies only to the income within that range.<br />3. The income ranges and tax rates are as follows - 0-10,000 at3% - 10,001−50,000at5−10,001-50,000 at5% - 50,001-100,000 at5.5%
4. The tax owed is the sum of the taxes calculated for each income range.
5. The final tax amount should be rounded to the nearest whole dollar.

STEP 2

First, we need to calculate the tax for the first income range ($0-10,000). This is done by multiplying the income in this range by the corresponding tax rate.
Tax0−10000=Income0−10000timesTax rate0−10000Tax_{0-10000} = Income_{0-10000} \\times Tax\, rate_{0-10000}

STEP 3

Now, plug in the given values for the income and tax rate in the first range to calculate the tax.
Tax0−10000=$10,000times3%Tax_{0-10000} = \$10,000 \\times3\%

STEP 4

Convert the percentage to a decimal value.
3%=0.033\% =0.03Tax0−10000=$10,000times0.03Tax_{0-10000} = \$10,000 \\times0.03

STEP 5

Calculate the tax for the first income range.
Tax0−10000=$10,000times0.03=$300Tax_{0-10000} = \$10,000 \\times0.03 = \$300

STEP 6

Next, we need to calculate the tax for the second income range ($10,001-50,000). This is done by multiplying the income in this range by the corresponding tax rate.
Tax10001−50000=Income10001−50000timesTax rate10001−50000Tax_{10001-50000} = Income_{10001-50000} \\times Tax\, rate_{10001-50000}

STEP 7

The income in the second range is the difference between 50,000and50,000 and 10,000. Plug in these values to calculate the tax.
Tax10001−50000=($50,000−$10,000)times5%Tax_{10001-50000} = (\$50,000 - \$10,000) \\times5\%

STEP 8

Convert the percentage to a decimal value.
5%=0.055\% =0.05Tax10001−50000=$40,000times0.05Tax_{10001-50000} = \$40,000 \\times0.05

STEP 9

Calculate the tax for the second income range.
Tax10001−50000=$40,000times.05=$2,000Tax_{10001-50000} = \$40,000 \\times.05 = \$2,000

STEP 10

Next, we need to calculate the tax for the third income range ($50,001-100,000). This is done by multiplying the income in this range by the corresponding tax rate.
Tax50001−100000=Income50001−100000timesTax rate50001−100000Tax_{50001-100000} = Income_{50001-100000} \\times Tax\, rate_{50001-100000}

STEP 11

The income in the third range is the difference between the total salary (60,000)and60,000) and 50,000. Plug in these values to calculate the tax.
Tax50001−100000=($60,000−$50,000)times5.5%Tax_{50001-100000} = (\$60,000 - \$50,000) \\times5.5\%

STEP 12

Convert the percentage to a decimal value.
5.5%=0.0555.5\% =0.055Tax50001−100000=$10,000times0.055Tax_{50001-100000} = \$10,000 \\times0.055

STEP 13

Calculate the tax for the third income range.
Tax50001−100000=$10,000times0.055=$550Tax_{50001-100000} = \$10,000 \\times0.055 = \$550

STEP 14

Now that we have the tax for each income range, we can sum these to find the total tax owed.
Total tax=Tax0−10000+Tax10001−50000+Tax50001−100000Total\, tax = Tax_{0-10000} + Tax_{10001-50000} + Tax_{50001-100000}

STEP 15

Plug in the values for the tax in each range to calculate the total tax.
Total tax=$300+$2,000+$550Total\, tax = \$300 + \$2,000 + \$550

STEP 16

Calculate the total tax owed.
Total tax=$300+$2,000+$550=$2,850Total\, tax = \$300 + \$2,000 + \$550 = \$2,850

STEP 17

Finally, round the total tax to the nearest whole dollar. Since the tax is already a whole dollar amount, no rounding is necessary.
Total tax=$2,850Total\, tax = \$2,850The state income tax owed on a 60,000peryearsalaryis60,000 per year salary is 2,850.

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