The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Example 9.2.5 Erik is paid biweekly. He is married, and claims three exemptions on
his tax return (one for himself, one for his wife, and one for a dependent child). After
he takes out his contributions for health insurance coverage and his 401(k), his gross
taxable pay is $1,535.06. How much should his employer withhold for federal income
taxes?

Each exemption is worth $126.92, so his three exemptions amount to (3)($126.92) 
$380.76. Subtracting this from his income leaves $1,535.06  $380.76  $1,154.30. For
this amount, his employer should withhold $57.30 plus 15% of the excess over $881, so
the withholding is $57.30  (0.15)($1,154.30  $881)  $57.30  (0.15)($273.30) 
$57.30  $41.00  $98.30.

The tax withholding tables are intended to make sure that enough money is withheld from
Erik’s paychecks to cover his income tax liability for the year. Unfortunately, there is much
that could affect the amount of taxes he owes in the end that these tables don’t—and couldn’t
reasonably be expected to—take into account. They are based on reasonable assumptions
for a typical taxpayer, but one size does not fit all. If Erik’s wife does not earn any income
from work outside of the home, they may be in a different tax bracket than if she earns a
large income. Erik may have income from work he does on the side, or income from invest-
ments. Or he may have made large contributions to charity, or paid a lot in mortgage inter-
est or medical expenses, and therefore claim much larger itemized deductions that could
make his ultimate tax total much lower than would be usual. None of these possibilities are
factored into his paycheck withholding. Regardless of the amount withheld, though, he is
still responsible for making sure that his tax withholding is adequate to cover his overall
tax bill.
If Erik expects that his withholding will not be enough to cover his ultimate tax bill, he may
be required to make estimated tax payments. Self-employed taxpayers, those who receive
much of their income from investments, or those whose tax withholding falls short of their
overall tax liability for whatever reason must make quarterly estimated tax payments, based
on their earnings for that quarter. If, however, he has just a moderate amount of additional
income and doesn’t want to be bothered with estimated tax payments, he can request that his
employer base withholding taxes on fewer exemptions or the higher single rate.

Example 9.2.6 Suppose that Erik fi les a new W-4 form claiming 0 exemptions and
requesting withholding at the higher single rate. How much would be withheld from his
paycheck in that case?

Using the single table and the full $1,535.06, we calculate that his withholding will be $156.55
plus 25% of the amount over $1,240. Thus the withholding is $156.55  (0.25)($1,535.06 
$1240)  $156.55  (0.25)($295.06)  $156.55  $73.77  $230.32. Note that this is
much higher than the withholding with three exemptions and the married rate.

Failing to have enough money withheld means facing a large tax bill later on, and also may
result in significant penalties. To avoid these unpleasant possibilities, claiming fewer than
the allowed number of exemptions and a single rather than married filing status is quite
commonly done.
Even though the withholding calculations presented here are indicative of how things
work in general, there are a number of other details that can affect the withholding rate.
(The IRS document that spells out all the details of withholding calculations is 68 pages in
length, which should give you a pretty good sense of the complexity involved.)

Tax Filing


Remember that the taxes withheld from your paycheck and/or estimated tax payments
that you make are not your actual income taxes. The income taxes that you owe for a year
can only be determined after the end of that year, once your total income and deductible
expenses are known. To determine your actual income taxes, each year you as a taxpayer
must file an income tax return with the Internal Revenue Service.

9.2 Income and Payroll Taxes 391
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