Rajesh is filing single and he has an adjusted gross income (AGI) of $\$ 94,000$ for the 2018 tax year. He qualifies for the standard deduction of $\$ 12,000$. Use the following 2018 Federal tax rate schedule to calculate his 2018 Federal income tax. If your filing status is single; \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} and taxable \\ income is more \\ than: \end{tabular} & \begin{tabular}{l} but not \\ over: \end{tabular} & your tax is: \\ \hline$\$ 0$ & $\$ 9,525$ & \begin{tabular}{l} $10 \%$ OF the taxable \\ income \end{tabular} \\ \hline$\$ 9,525$ & $\$ 38,700$ & \begin{tabular}{l} $\$ 952.50$ plus $12 \%$ of the \\ excess over $\$ 9,525$ \end{tabular} \\ \hline$\$ 38,700$ & $\$ 82,500$ & \begin{tabular}{l} $\$ 4,453.50$ plus $22 \%$ of the \\ excess over $\$ 38,700$ \end{tabular} \\ \hline$\$ 82,500$ & $\$ 157,500$ & \begin{tabular}{l} $\$ 14,089.50$ plus $24 \%$ of \\ the excess over $\$ 82,500$ \end{tabular} \\ \hline$\$ 157,500$ & $\$ 200,000$ & \begin{tabular}{l} $\$ 32,089.50$ plus $32 \%$ of \\ the excess over $\$ 157,500$ \end{tabular} \\ \hline$\$ 200,000$ & $\$ 500,000$ & \begin{tabular}{l} $\$ 45,689.50$ plus $35 \%$ of \\ the excess over $\$ 200,000$ \end{tabular} \\ \hline$\$ 500,000$ & & \begin{tabular}{l} $\$ 150,689.50$ plus $37 \%$ OF \\ THE AMOUNT OVER \\ $\$ 500,000$ \end{tabular} \\ \hline \end{tabular} Rajesh's 2018 tax is: \$ (Round to the nearest dollar.) What is Rajesh's effective tax rate? [Tax paid divided by taxable income] (Write as a percent, rounded to one decimal place.)
Solution
Step 1 ：Calculate Rajesh's taxable income by subtracting the standard deduction from his adjusted gross income (AGI). The formula is \(\text{Taxable income} = \text{AGI} - \text{Standard deduction}\). Substituting the given values, we get \(\text{Taxable income} = $94,000 - $12,000 = $82,000\).
Step 2 ：Next, calculate his tax based on the tax rate schedule. His taxable income falls into the third bracket ($38,700 to $82,500), so his tax is calculated as follows: \(\text{Tax} = $4,453.50 + 22\% \text{ of the excess over } $38,700\). Substituting the given values, we get \(\text{Tax} = $4,453.50 + 22\% * ($82,000 - $38,700) = $4,453.50 + 22\% * $43,300 = $4,453.50 + $9,526 = $13,979.50\). Rounding to the nearest dollar, Rajesh's 2018 tax is \(\boxed{$13,980}\).
Step 3 ：Finally, calculate Rajesh's effective tax rate by dividing the tax paid by his taxable income and multiplying by 100 to get a percentage. The formula is \(\text{Effective tax rate} = (\text{Tax paid} / \text{Taxable income}) * 100\). Substituting the given values, we get \(\text{Effective tax rate} = ($13,980 / $82,000) * 100 = 17.04878\%\). Rounding to one decimal place, Rajesh's effective tax rate is \(\boxed{17.0\%}\).
