income total spending
$10,000 $10,000
20,000 18,000
50,000 35,000
100,000 60,000
If a sales tax of ten percent is levied on all purchases, calculate
A. amoust of sales tax paid at each income level and
B. the fraction f income paid in taxes at each income level
Let X be pre-tax spending. For a total spending of 10000 = 1.1*X. Solve for X. X=9090.90 Meaning sales tax must be 909.1. Repeat for all other total spending levels.
To calculate the amount of sales tax paid at each income level, we can use the formula:
Sales Tax = Total Spending - (Total Spending / (1 + Tax Rate))
Given that the tax rate is 10 percent (0.10), we can calculate the sales tax for each income level:
For income level 1: Total Spending = $10,000
Sales Tax = $10,000 - ($10,000 / (1 + 0.10))
Sales Tax = $10,000 - $9,090.91
Sales Tax = $909.09
For income level 2: Total Spending = $18,000
Sales Tax = $18,000 - ($18,000 / (1 + 0.10))
Sales Tax = $18,000 - $16,363.64
Sales Tax = $1,636.36
For income level 3: Total Spending = $35,000
Sales Tax = $35,000 - ($35,000 / (1 + 0.10))
Sales Tax = $35,000 - $31,818.18
Sales Tax = $3,181.82
For income level 4: Total Spending = $60,000
Sales Tax = $60,000 - ($60,000 / (1 + 0.10))
Sales Tax = $60,000 - $54,545.45
Sales Tax = $5,454.55
To calculate the fraction of income paid in taxes at each income level, we divide the sales tax by the income:
For income level 1: Fraction of Income paid in Taxes = $909.09 / $10,000 = 0.0909 = 9.09%
For income level 2: Fraction of Income paid in Taxes = $1,636.36 / $20,000 = 0.0818 = 8.18%
For income level 3: Fraction of Income paid in Taxes = $3,181.82 / $50,000 = 0.0636 = 6.36%
For income level 4: Fraction of Income paid in Taxes = $5,454.55 / $100,000 = 0.0545 = 5.45%
Therefore, the amount of sales tax paid and the fraction of income paid in taxes at each income level are as follows:
Income Level 1: Sales Tax = $909.09, Fraction of Income paid in Taxes = 9.09%
Income Level 2: Sales Tax = $1,636.36, Fraction of Income paid in Taxes = 8.18%
Income Level 3: Sales Tax = $3,181.82, Fraction of Income paid in Taxes = 6.36%
Income Level 4: Sales Tax = $5,454.55, Fraction of Income paid in Taxes = 5.45%