Question

dr. jones lives in a country with a progressive tax system. that is, he does not pay any taxes on the first $\$20{,}000$ in income he makes, he pays $5\%$ taxes on the next $\$25{,}000$, he pays $10\%$ taxes on the next $\$35{,}000$, he pays $15\%$ on the next $\$50{,}000$, and he pays $20\%$ on every additional dollar onwards. if dr. jones pays $\$10{,}000$ in taxes, then how much income does he make?

Answer 1

To find Dr. Jones's income with a tax payment of $10,000 in a progressive tax system, the taxes paid at each income bracket must be calculated. Adding the untaxed income and income from each bracket leads to a total income of $115,000.

Step-by-step explanation:

Dr. Jones lives in a country with a progressive tax system, which means his income is taxed at increasing rates as his income surpasses certain thresholds. To calculate Dr. Jones's income based on the tax he pays, we must consider each income level and its associated tax rate sequentially until his total tax payment reaches $10,000.

Let's break down the income levels and corresponding taxes:

No tax on first $20,000

$20,001 to $45,000: 5% tax

$45,001 to $80,000: 10% tax

$80,001 to $130,000: 15% tax

Over $130,000: 20% tax (Not yet applicable)

First, calculate the taxes for each bracket, before Dr. Jones's marginal tax rate exceeds 15%, as follows:

$25,000 at 5% = $1,250

$35,000 at 10% = $3,500

Next, find the amount taxed at 15%. To do this, subtract the tax already paid ($1,250 + $3,500 = $4,750) from the total tax paid ($10,000) to determine the tax paid at the 15% rate: $10,000 - $4,750 = $5,250.

Finally, calculate the amount of income that would be taxed at 15% to result in $5,250 of taxes: $5,250 / 0.15 = $35,000.

Now, add up all the amounts untaxed and taxed at various rates to find Dr. Jones's total income:

$20,000 (untaxed) + $25,000 (5%) + $35,000 (10%) + $35,000 (15%) = $115,000

Therefore, Dr. Jones's total income is $115,000.