# In the following scenario, if Kate has a taxable income of $100,520, how much tax will she pay? Figure out how much income tax each of the following individual The marginal tax rates are...

In the following scenario, if Kate has a taxable income of $100,520, how much tax will she pay?

Figure out how much income tax each of the following individual The marginal tax rates are structured as follows:

Income up to $42,350 is taxed at 15 percent

Income earned between 42,350 and $61,400 is taxed at 28 percent.

Income between $61,401 and $128,100 is taxed at 31 percent

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### 2 Answers

In this case, many people think that Kate’s tax liability is simply calculated by multiplying her taxable income by the tax rate for people who are making that much money. In other words, they would say we would figure Kate’s tax by multiplying her taxable income by 31 percent. That would get us

100,520*.31 = 31,161.20

But that is not correct, Kate does not pay this much tax. The reason is that the marginal tax system works differently. The money that Kate (or anyone) makes between certain amounts is all taxed at a different rate. As the question tells us, the first $42,350 of someone’s income is taxed at 15%. Kate has more than $42,350 of income. Therefore, she has a full $42,350 to be taxed at that rate. We find out how much she has to pay on that income with the following equation:

42,350*.15 = 6352.5

Now, Kate also has income in the next tax bracket. All income between $42,351 and and $61,400 is taxed at 28%. First, we have to find out how much money Kate makes in this bracket. Since she makes more than 61,400, we find that through this equation:

61,400 – 42351 = 19,049.

Now, we need to multiply that amount of income by 28%. That equation is as follows:

19,050*.28 = 5333.72

Finally, we know that Kate has income in the 31% bracket. First, we have to find out how much income she has in that bracket. We do that with this equation:

100,520 – 61,401 = 39,119

Now, we find out how much tax she pays on that income by multiplying it by 31%. That is shown in the following equation.

39,119*.31 = 12,126.89

Now we know how much Kate pays for each chunk of her income. We now have to add together all of the taxes she paid on all of the chunks. We use the following equation

12,126.89 + 5333.72 + 6352.5 = 23,813.11

So, instead of paying over $31,000, Kate actually pays more than $7,000 less than that.

**Kate’s tax liability, then, is $23,813.11.**

The rate at which income earned is taxed increases with an increase in the taxable income. In most nations the increased rate of taxation is not applicable for the entire income earned, instead several tax brackets are created with a progressively higher rate of taxation. The information provided in the question gives the rate of taxation as:

15% for income up to $42350.

28% for income earned between $42350 and $61400

31% for income between $61401 and $128100

Kate's income is $100520.

The tax paid by her for the first $42350 earned is 0.15*42350 = $6352.5

The tax paid on the income lying between $42350 and $61400 is 0.28*19050 = $5334

The rest of her income i.e. 100520 - 61400 = $39120 is taxed at 31%; this gives the tax to be paid as $12127.2

The total amount to be paid as income tax is $6352.5 + $5334 + $12127.2 = $23813.7