Question

tim mogilnitsky is a self - employed researcher. he pays fica at a rate of 12.4% and medicare at a rate of 2.9%. find the dollar amount of these taxes on the annual adjusted earnings of $42,986.35. tims fica tax is $\square$ (round to the nearest cent.)

Explanation:

Step1: Calculate total tax rate

First, find the total tax rate by adding the FICA rate and the Medicare rate. The FICA rate is 12.4% and the Medicare rate is 2.9%, so the total rate is \(12.4\% + 2.9\% = 15.3\%\). Convert this percentage to a decimal by dividing by 100, so \(15.3\% = 0.153\).

Step2: Calculate total tax amount

Multiply the annual adjusted earnings by the total tax rate. The annual adjusted earnings are $42,986.35. So the tax amount is \(42986.35\times0.153\).
Calculating this: \(42986.35\times0.153 = 42986.35\times(0.1 + 0.05 + 0.003)=42986.35\times0.1 + 42986.35\times0.05 + 42986.35\times0.003 = 4298.635 + 2149.3175 + 128.95905 = 6576.91155\).

Step3: Round to nearest cent

Round the result to the nearest cent. The number \(6576.91155\) rounded to the nearest cent is \(6576.91\) (since the third decimal is 1, which is less than 5, we round down the second decimal). Wait, wait, actually, let's check the multiplication again. Wait, \(42986.35\times0.153\):
Let's do the multiplication properly: \(42986.35\times0.153\)
First, \(42986.35\times0.1 = 4298.635\)
\(42986.35\times0.05 = 2149.3175\)
\(42986.35\times0.003 = 128.95905\)
Adding them together: \(4298.635 + 2149.3175 = 6447.9525\); \(6447.9525 + 128.95905 = 6576.91155\). Now, the second decimal is 1, the third is 1, so when rounding to the nearest cent (two decimal places), we look at the third decimal which is 1, so we keep the second decimal as is. Wait, no, 6576.91155: the first decimal is 9, second is 1, third is 1. Wait, no, 6576.91155 is 6576 dollars, 91 cents, and 1.155 mills. So rounding to the nearest cent, since the thousandth place is 1 (less than 5), we round down, so it's 6576.91? Wait, no, wait 6576.91155: the decimal part is 0.91155. So the first decimal is 9 (tenths place), second is 1 (hundredths place), third is 1 (thousandths place). So when rounding to the nearest cent (hundredths place), we look at the thousandths place, which is 1, so we don't round up the hundredths place. So it's 6576.91? Wait, but let's check with a calculator: 42986.35 0.153. Let's compute 42986.35 0.153:

42986.35 * 0.153:

First, 42986.35 153 = 42986.35 (150 + 3) = 42986.35150 + 42986.353 = 6447952.5 + 128959.05 = 6576911.55

Then divide by 1000 (since 0.153 = 153/1000) : 6576911.55 / 1000 = 6576.91155. So yes, that's correct. So rounding to the nearest cent, it's $6576.91. Wait, but wait, maybe I made a mistake in the tax rates? Wait, self-employed individuals pay FICA (Social Security and Medicare) taxes at a rate of 15.3% (12.4% for Social Security and 2.9% for Medicare), which is correct. So the calculation is correct.

Answer:

\(6576.91\)