Question

Bert earns $35,000 gross annual salary. In Bert's jurisdiction there is a progressive tax system with rules as follows: Any amounts earned up to $20,000 are taxed at x%. Any amounts earned beyond $20,000 are taxed at 20%. Given that Bert pays $4,500 per annum in income tax, calculate x. Give your answer to the nearest tenth of a percent. Do not include the percent symbol in your answer.

Answer 1

The tax rate x% at which Bert's first $20,000 income is taxed is calculated by subtracting the tax paid on the amount above $20,000 from his total tax and dividing it by $20,000. The result is 7.5%.

Step-by-step explanation:

To calculate the tax rate x% at which the first $20,000 of Bert's income is taxed, we need to know his gross salary and the amount of tax he pays. As Bert earns a gross annual salary of $35,000 and the tax rules in his jurisdiction dictate that any amounts earned beyond $20,000 are taxed at 20%, we can calculate how much tax he pays on the income over $20,000 and thus determine the tax on the first $20,000.

Bert pays tax on the $15,000 above $20,000 at the rate of 20%, which amounts to $15,000 * 20% = $3,000. Since Bert pays a total of $4,500 annually in income tax, the tax on the first $20,000 is $4,500 - $3,000 = $1,500. To find the tax rate x for the first $20,000, we calculate $1,500 / $20,000 = 0.075, or 7.5%. Thus, x to the nearest tenth of a percent is 7.5.