Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.2 Income Tax - Exercise Set 8.2 - Page 506: 7

Answer

Tax owed is \[\$26,765.25\].

Work Step by Step

In this case, it is required to compute the tax owed by a single man with a taxable income of \[\$120,000\], the percentage deducted on the first \[\$8,700\] is \[10%\] \[\begin{align} & \text{Tax}\ \text{liability}\ \text{on}\ \text{first}\ \$8700=\text{Rate}\times\text{Income}\\&=0.8\times\$8,700\\&=\$870\end{align}\] \[10%\]and till the next \[\$35,350\] is \[15%\], i.e.,\[35,350-8,700=26,650\] \[\begin{align} & \text{Tax}\ \text{liability}\ \text{on}\ \text{the}\ \text{next}\ \$26,650=\text{Rate}\\times\\text{Income}\\&=0.15\times\$26,650\\&=\$3,997.5\end{align}\] Till the next \[\$71,350\]is \[25%\], i.e.,\[71,350-35,350=36,000\] \[\begin{align} & \text{Tax}\ \text{liability}\ \text{on}\ \text{the}\ \text{next}\ \$36,000=\text{Rate}\times\text{Income}\\&=0.25\times\$36,000\\&=\$9000\end{align}\] Till the next \[\$108,725\]is \[28%\], i.e.,\[108,725-75,950=32,775\] \[\begin{align} & \text{Tax}\ \text{liability}\ \text{on}\ \text{the}\ \text{next}\ \$32,775=\text{Rate}\times\text{Income}\\&=0.28\times\$32,775\\&=\$9177\end{align}\] And the remaining is \[120,000-108,725=11275\]and the tax is \[33%\]: \[\begin{align} & \text{Tax}\ \text{liability}\ \text{on}\ \text{the}\ \text{next}\ \$11,275=\text{Rate}\times\text{Income}\\&=0.33\times\$11,275\\&=\$3720.75\end{align}\] The sum of tax liabilities will be the total tax owed by the person. \[\begin{align} & \text{Total}\ \text{Tax}\ \text{owed}=\$870+\$3,997.5+\$9000+\$9177+\$3720.75\\&=\$26,765.25\end{align}\]
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