22. Gross income = $3,452,000 + $54,200 = $3,506,200. Adjusted gross income = $3,506,200 - $30,000 = $3,476,200. Taxable income = $3,476,200 - $674,500 = $2,801,700.
28. Emily and Juan's gross income is $75,300 + $2000 + $1650 = $78,950 (wages plus rental income plus interest). Their contribution to a tax-deferred plan makes their AGI (adjusted gross income) $78,950 - $3240 = $75,710. Their exemptions total 4 × $3050 - $12,200, and they should use their itemized deductions of $9610 because it is greater than the standard deduction of $9500. So their taxable income is $75,710 - $12,200 = $53,900.
36. Chris is in the 33% marginal tax bracket for married people filing separately. Her first $7000 is taxed at 10%, the next $(28,400-7000) = $21,400 is taxed at 15%, the next $(57,325-28,400) = $28,925 is taxed at 25%, the next $(87,350-57325) = $30,025 is taxed at 28%, and the remaining $(127,300-87,350) = $39,950 is taxed at 33%. Her tax bill is 0.10(7000) + 0.15(21,400) + 0.25(28,925) + 0.28(30,025) + 0.33(39,950) = 0.10*(7000) + 0.15*(21400) + 0.25*(28925) + 0.28*(30025) + 0.33*(39950) = $32,731.75.
42. Santana's $1000 charitable contribution reduces her taxable income by $1000, so she will save 35% of $1000 or $350. (Unless she is right at the bottom of the 35% bracket, and the $1000 contribution reduces her her taxable income into the 33% bracket, in which case her savings will be somewhere between $330 and $350.
44. The apartment rent is $600 per month. The house mortage payments cost $675 per month, of which the interest of $675 is tax deductible. This will save you 15% × $600 = $90, so that the true monthly cost of the mortgage is $675 - $90 = $585. Thus, buying the house is actually cheaper, at least for now!
46. The $4000 that each of Yalanda and Alia donate to charity is tax deductible. This will save Yolanda 35% × $4000 = $1400, so that the true cost to her is $4000 - $1400 = $2600. Alia, meanwhile, saves 10% × $4000 = $400, so that the true cost to her is $4000 - $400 = $3600. The true cost of the donation to charity is lower for Yolanda because of her higher tax bracket.
52. Larae's salary of $21,200 is subject to the usual FICA tax: 7.65% × $21,200 = $1622. To find her taxable income we subtract the $3050 personal exemption and $4750 standard deduction from her salary: $21,200 - $3050 - $4750 - $13,400. Her federal tax is 0.10($7000) + 0.15($13,400-$7000) = $1660. Thus Larae's FICA tax and income tax total is $1622 + $1660 = $3282. Since $3282/$21,200 = 0.1548, her overal tax rate is 15.48%.
54. Deion has only ordinary income and no capital gains;
his gross income and adjusted gross income are $60,000, all of
which is subject to FICA tax and income tax. The FICA tax is
7.65% × $60,000 = $4590. To find his income tax, first
subtract the $4750 standard deduction and $3050 personal exemption
to get his taxable income: $60,000 - $4750 - $3050 = $52,200.
This puts Deion in the 25% marginal tax bracket as a single person.
His income tax is 0.10($7000) + 0.15($28,400-$7000) + 0.25($52,200-$28,400)
= $9860. Thus Deion's FICA tax and income tax total is $4590+$9860
= $14,450. Since $14,450/$60,000 = 0.2408, his overall tax rate
is 24.08%.
By contrast, Joesphina has all of her $60,000 income in capital gains.
She owes no FICA taxes. Her gross income can be reduced by the $4750
standard deduction and $3050 personal exemption to give her taxable
income: $60,000 - $4750 - $3050 = $52,200. As capital gains for a
single person, this income is taxed at 5% for the first $7000 and
the remainder at 15%. So Josephina's income tax is
0.05($7000) + 0.15($52,200-$7000) = $7130. Since $7130/$60,000 =
0.1188, her overal tax rate is 11.88%.
Although Deion and Josephina have the same gross income, Josephina pays
half of what Deion pays in taxes because her income consists of capital gains.
58. With a taxable income of $200,000, your marginal tax rate is 33%. Thus each $800 contribution to a tax-deferred savings plan will reduce your tax bill by 0.33 × $800 = $264. In other words, $800 will go into your tax-deferred savings account each month, but your monthly paychecks will decrease by only $800 - $264 = $536. Annually, you will take home 12 × $264 = $3168 more pay.
Section 4E:
16.
(a) The total of your outlays is $8000 + $4500 + $1600 + $10,400 =
$24,500, which is less than your net income of $28,000, so you have
a comfortable surplus.
(b) Your projected outlays for next year total $8000 + $4500 + $1600
+ $10,400 + $5200 = $29,700, while your income is expected to be
102% × $28,000 = $28,560, which is smaller Hence, you will not
be able to pay off the credit card debt of $5200.
(c) In this scenario, your projected outlays for next year total
101% × ($8000 + $4500 + $1600 + $10,400) + $3500 = $28,245.
This is $315 less than your projected income of $28,560, so you
can just afford the additional $3500 for the wedding and honeymoon!
20.
(a) Assuming an interest rate of 8.2%, the 2005 interest payment
will be 8.2% × $773,000 (see Example 3), which is roughly $63,000.
(b) The total outlays for 2005 come to $850,000+$290,000+$210,000
plus the $63,000 interest payment (see above) on the debt as it stood
at the end of 2004; these all add up to $1,413,000.
The year-end surplus-or-deficit is the $975,000 in total receipts
for 2005 less the $1,413,000 total outlays for that year; this is
a deficit of $438,000.
At the end of the 2005, the accumulated debt now stands at
$773,000 + $438,000 = $1,211,000.
(c) Assuming an interest rate of 8.2% for the next year,
the 2006 interest payment will be 8.2% × $1,211,000,
which is about $99,000.
I've started to wonder if anyone reads these solutions that I prepare.
So, the first Math 141 student who emails me to tell me that they have
read this paragraph will get $1! Send email to propp@math.wisc.edu .
(d) The total outlays for 2006 will come to $850,000 + $290,000
plus the $99,000 interest payment (see above) on the debt as it
stood at the end of 2005; these all add up to $1,239,000.
The year-end surplus-or-deficit will be the $1,050,000 in
total receipts for 2006 less the $1,239,000 total outlays for
that year; this is a deficit of $189,000.
At the end of 2006, the accumulated debt will stand at
$1,211,000 + $189,000 = $1,400,000.
22. The total receipts for 2002 were $1853 billion.
A 0.5% decrease in total receipts would have led to a
0.5% × $1853 billion, or $10 billion, increase in the
deficit, so that the deficit would have been about $158 + $10
= $168 billion.
The total outlays for 2002 were $2011 billion. A 1% increase
in total outlays would have led to a 1% × $2011 billion,
or $20 billion, increase in the deficit, so that the deficit
would have been about $158 + $20 = $178 billion.
26. Social Security accounted for 22% × $2011 billion = $442 billion of the total outlays.
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