15.5: Chapter 6
- Page ID
- 129935
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Your Turn
6.1
1. \(\frac{3}100\)
2. \(\frac94100\)
3. \(\frac67.2100\)
4. \(\frac670100\)
6.2
1. 0.09
2. 0.24
3. 0.0218
6.3
1. 41%
2. 2%
3. 924.81%
6.4
1. 338
2. 2058.75
6.5
1. 250
2. 6,000
6.6
1. 62.5%
2. 40%
6.7
1. $529.50
6.8
1. 66.31%
6.9
1. 80 bulbs.
6.10
1. Discount is $496; sale price is $1,054.00
2. Discount is $2.75; sale price is $24.75
6.11
1. 35%
2. 12%
6.12
1. $13.00
2. $220.00
6.13
1. Discount is $330; sale price of the bed is $220.
6.14
1. 15%
6.15
1. $59.00
6.16
1. Markup is $396; retail price is $2,196.00.
2. Markup is $1.05; retail price is $11.55.
6.17
1. 58.33%
2. 200%
6.18
1. $35.00
2. $8.99
6.19
1. The retail price of the bed is $1,260.00.
6.20
1. 24%
6.21
1. $38.00
6.22
1. Sales tax is $104.93; total price is $1,603.93.
2. Sales tax is $1.88; total price is $28.77.
6.23
1. Sales tax rate = 5.25%
2. Sales tax rate = 6.75%
6.24
1. $145.78
2. $489.00
6.25
1. Sales tax is $111.22. The total price Daryl pays is $1,260.22.
6.26
1. The sales tax is $9.
6.27
1. Interest = $2,409.99, the loan payoff is $9,109.99
2. Interest = $8,901, the loan payoff is $34,701.00
6.28
1. She will pay $878.75 in interest, total repayment is $10,378.75.
6.29
1. He will pay $727.86 in interest, payoff is $9,127.86.
6.30
1. The cost to borrow is $115.51 and their payoff is $3,815.51.
6.31
1. Interest = $253.8, \(FV\) = $4,753.80
2. Interest = $406.00, \(FV\) = $2,406.00
3. Interest= $1019.18, \(FV\) = $121,019.18
4. Interest = $253.89, \(FV\) = $4,933.89
6.32
1. Mia will receive $6,254.85.
6.33
1. $846.58
2. $172.91
6.34
1. $709.59
2. $13,182.74
6.35
1. $2,313.74
6.36
1. $443.90
6.37
1. $14,285.72. $14,285.72 needs to be invested so that, after 10 years at 7.5% interest, the investment will be worth $25,000.
2. $97,709.93. $97,709.93 needs to be invested so that, after 35 years at 6.5% interest, the investment will be worth $320,000.
3. $48,813.56. $48,813.56 needs to be invested so that, after 270 months at 3.75% interest, the investment will be worth $90,000.
6.38
1. $10,549.46
6.39
1. The CD is worth $5,627.54 after 4 years.
6.40
1. CD would have been worth $5,600. Oksana earned $27.54 more with compound interest.
6.41
1. $11,443.81
2. $26,551.23
6.42
1. $5,813.64
6.43
1. $3,555.88
6.44
1. $100,811.07
2. $82,135.75
6.45
1. $96,271.23
6.46
1. A rate of 7% compounded quarterly is equivalent to a simple interest rate of 7.19%.
6.47
1. The effective annual yield is 2.53%.
6.48
1. The effective annual yields for the banks are 3.1158% for Smith Bank, 3.11% for Park Bank, 3.1381% for Town Bank, and 3.144% for Community Bank. Community Bank has the best yield.
6.49
1. Mateo’s budget is below.
His total monthly income is $3,675.00, and his monthly expenses are $3,775. Mateo falls $100.00 short each month.
| Income Source | Amount | Expense | Amount |
|---|---|---|---|
| Electrician | $3,375.00 | Mortgage | $987 |
| Side jobs | $300.00 | Truck payment | $589 |
| Truck insurance | $312 | ||
| Utilities | $167 | ||
| Clothing | $150 | ||
| Entertainment | $400 | ||
| Credit Card | $325 | ||
| Food | $470 | ||
| Gasoline | $375 |
6.50
1. Maddy’s budget is below.
Her total monthly income is $6,093.75, and her monthly expenses are $4,389.27. Maddy has $1,704.48 in extra income per month. This is her cushion in the budget.
| Income Source | Amount | Expense | Amount |
|---|---|---|---|
| Engineer | $6,093.75 | Mortgage | $1,452.89 |
| Car payment | $627.38 | ||
| Car insurance | $179.00 | ||
| Health Insurance | $265.00 | ||
| Utilities | $320.00 | ||
| Clothing | $150.00 | ||
| Entertainment | $400.00 | ||
| Credit Card | $450.00 | ||
| Food | $370.00 | ||
| Gasoline | $175.00 |
Her total monthly income is $6,093.75, and her monthly expenses are $4,389.27. Maddy has $1,704.48 in extra income per month. This is her cushion in the budget.
6.51
1. Heather’s budget is now
The changes have added $355.00 to her budget. As her extra income is $601.40, she can afford the changes.
| Income Source | Amount | Expense | Amount |
|---|---|---|---|
| Nursing | $3,765.40 | Mortgage | $1,240 |
| Part-time | $672.00 | Car Payment | $489 |
| Student Loan | $728 | ||
| Car Insurance | $139 | ||
| Utilities | $295 | ||
| Clothing | $150 | ||
| Entertainment | $300 | ||
| Credit Card | $200 | ||
| Food | $400 | ||
| Gasoline | $250 |
6.52
1. Heather’s total income is $4,437.40.
For the necessities, Heather should budget $2,218.70.
For her wants, she should budget $1,331.22.
For savings and extra debt service, she should budget $887.48.
Her necessities total $3,536.00, which exceeds the suggested budget amount of $2,218.70.
Her wants total $300.00, which is below the suggested budget amount of $1,331.22.
Her excess income is $601.40, which is below the suggested budget amount of $887.48.
Heather should make some changes.
For the necessities, Heather should budget $2,218.70.
For her wants, she should budget $1,331.22.
For savings and extra debt service, she should budget $887.48.
Her necessities total $3,536.00, which exceeds the suggested budget amount of $2,218.70.
Her wants total $300.00, which is below the suggested budget amount of $1,331.22.
Her excess income is $601.40, which is below the suggested budget amount of $887.48.
Heather should make some changes.
6.53
1. Elijah should budget $1,631.72 for needs, $979.03 for wants, and $652.69 for savings and debt service. When choosing where to live, what to eat, and what to drive, he should make choices that keep those costs, combined with debt service costs, gasoline, and utilities, below $1,631.72. This means he will have to make decisions about what his priorities are. Elijah should then figure out his wants, and stay within the limits here, that is, keep those costs below $979.03. Finally, he can begin to build his savings with the remaining $652.69.
6.54
1. Her monthly income is $3,641.66.
Needs (50%): $1,820.83, Wants (30%): $1,092.50, Savings (20%): $728.33
Needs (50%): $1,820.83, Wants (30%): $1,092.50, Savings (20%): $728.33
2. $1,061.83
3. $1,092.50, $728.33
4. She only has budgeted $1,061.83 for other necessities. It is difficult to imagine Fran being able to afford to change jobs and move, unless she reallocates money that she would want to save or use for entertainment or takes on another job. If Fran uses all the money that the 50-30-20 budget sets aside for savings, she then would have $1,790.16 to spend on those other necessities. If she moves away from the 50-30-20 philosophy, she may be able to afford the move. However, that means changing her priorities.
6.55
1. $5,952.97
6.56
1. $3,741.46
6.57
1. $8,978.57
6.58
1. 17.31%
2. 13.2%
6.59
1. $42,499.63
6.60
1. $93,037.59
6.61
1. $1,227.30
6.62
1. $237.50 per year, $5,237.50 on maturity date.
6.63
1. $108,501.30
6.64
1. 4.28%
2. 3.29%
6.65
1. Looking at the table, the current price of a share is $30.68.
2. The high was $56.28, and the low was $30.05.
3. August 4, 2022
4. 4.77%
5. $4.66
6.66
1. $336.00
6.67
1. $52
2. 2.6%
6.68
1. $108,352.43
6.69
1. $1,815.83
6.70
1. 23.75%
6.71
1. 4.35%
6.72
1. 371.74%
2. 13.8%
6.73
1. $3,336.13
6.74
1. Traditional
6.75
1. $5,460
2. $10,920
3. 100% return on the $5,460 deposit
6.76
1. $813,128.60
2. $457,384.83
6.77
1. $355.91
2. $62.48
6.78
1. $213.07
2. $209.96
6.79
1. $34,700, 3.79%, 6 years
2. $539.57
3. $25,837.42
4. $104.14
5. $2,246.62
6. The amount paid to principal increases each month
6.80
1. $6,437.18
6.81
1. $9,745
6.82
1. Tiana can take out $12,500, the maximum in year 6.
6.83
1. Gap = $10,850, Federal loans = $7,500, Remaining $3,350
6.84
1. $2,987.63
6.85
1. $82.70
2. $137.42
6.86
1. $259.69
6.87
1. There is no impact on Ryann’s interest rate. The total Ryann pays back increases since the interest is extended to more periods.
6.88
1. $188.03
6.89
1. $5,310
6.90
1. $11,735
2. $97.80
6.91
1. Store-issued credit cards
2. Fees (both annual and penalty fees), reward programs, credit limits
3. Travel and entertainment cards
6.92
1. April 01 2015 to April 30 2015
2. $9,000.00
3. $5.99
6.93
1. $567.32
6.94
1. $22.64
2. $13.49
3. $77.77
6.95
1. $566.44
2. $3,267.17
6.96
1. $1,152.35
6.97
1. $47.47
2. $84.00
3. $19.90
6.98
1. $33,838.48
6.99
1. $32,777.75
6.100
1. $436.70
2. $649.47
6.101
1. $1,516.05
6.102
1. $10,567.00
6.103
1. $401.05
6.104
1. 6.25%
2. \(0.00003291\overline 6 \)
6.105
1. $74.49
2. $1,015.25
6.106
1. Purchase
2. Purchase
6.107
1. Personal injury protection
2. Liability insurance
6.108
1. $593.36
6.109
1. $42.02
6.110
1. $949.72
6.111
1. $319,620.60
6.112
1. $93,741.60
6.113
1. 6.1%
2. $1,383.61
3. $730.38
4. $723.66
5. $133,513.05
6. Payment 225
6.114
1. $1,521.20
6.115
1. $47,280
6.116
1. $80,300
6.117
1. $39,700
6.118
1. $25
6.119
1. Refund of $1,920
6.120
1. FICA is $244.80, SSI is $198.40
6.121
1. $9,114
6.122
1. $11,787
6.123
1. His credits exceed his taxes owed, so he receives a refund, which is for $1,673.94.
Check Your Understanding
1. 100
2. 0.387
3. 190.4
4. 834.15 (rounded to two decimal places)
5. 24.07%
6. 16 new drivers will be hired.
7. a reduction in price
8. the amount a retailer adds to the cost of goods to cover overhead and profit
9. $30.60
10. $497.60
11. Yes
12. $42.67
13. Interest is money paid by a borrower to a lender for the privilege of borrowing money.
14. The amount borrowed is the principal.
15. $1,169.10
16. $11,374.87
17. $266.82
18. $21,818.19
19. interest that is earned on both the principal and the interest from previous periods
20. compound
21. $15,698.69
22. $405.62
23. $30,266.48
24. Compare their effective annual yield.
25. 4.98%
26. A budget is an estimation of income and expenses over some period of time.
27. Expenses that represent basic living requirement and debt service.
28.
| Income | Amount | Expenses | Amount |
|---|---|---|---|
| Job | $3,450.00 | Rent | $925.00 |
| Car payment | $178.54 | ||
| Car insurance | $129.49 | ||
| Credit card | $117.00 | ||
| Gas | $195.00 | ||
| Food | $290.00 | ||
| Amazon Prime | $21.99 | ||
| Internet | $49.99 | ||
| Going out | $400.00 | ||
| Total | $2,307.01 |
29. $1,142.99
30. David should allocate $1,735 to necessary expenses, $1,035 to expenses that are wants, and $690 to savings and extra debt service.
31. David spends $1,835.03 on necessary expenses, which is fairly close to the 50-30-20 budget philosophy guidelines. He spends $471.98 on expenses that are wants, which is well below the guideline of $1,035. He has $1,149.99 in extra income, which is well above the savings and debt service guidelines.
32. A deposit account, held at a bank or other financial institution, which bears some interest on the deposited money.
33. Once money is deposited in a CD, the money cannot be withdrawn until the end of the CD period.
34. A money market account is more flexible. Transactions can be made after creating the money market account.
35. $8,549.93
36. 25.6%
37. $21,441.03
38. $2,030.65
39. Stocks
40. Income must be below a threshold for a person to use a Roth IRA.
41. They invest in different investment vehicles so that no single investment can have a large impact on the value of the mutual fund.
42. Each year, the holder of the bond receives $200. For 10 years, that’s $2,000 total earned with the bond.
43. Yes
44. $3,500, which is 4% of her income
45. $114.00
46. 9.93%
47. $5,207.59
48. Varies
49. Loan with a fixed period, and the borrower pays a fixed amount per period until the loan is paid off
50. More is applied to the principal.
51. $59.11
52. $2,233.12
53. $42,962.51
54. $39,544.50
55. Spring (March) before the start of the fall term
56. 9 years
57. The difference between the cost of college (including books, fees, room and board, etc.) and all non-loan financial aid they receive
58. In subsidized loans, the interest does not accrue while the student is still in school. In unsubsidized student loans, the interest begins accruing as soon as the money is disbursed.
59. $31,000
60. $13,028.61
61. 10 years
62. 10%
63. Bank issued, store issued, charge (Travel/entertainment) cards
64. Store issued
65. Due date, minimum payment due, and balance due
66. $19.30
67. $4,104.27
68. $696.21
69. Cost of delivering the vehicle to the dealer
70. Registers your car with the state, gets the license plate, and assigns the title of the car to the lender
71. $628.89
72. Interest rate higher loan term shorter
73. Title and registration, documentation fee, sales tax
74. $333.34
75. 3.75%
76. Purchasing
77. Cover the damage caused to your car if involved in an accident with another vehicle
78. Buying
79. Renting
80. Buying
81. Mortgage
82. $663.32
83. $129,802.20
84. $554.06
85. Escrow
86. Any and all income, including wages, salary, interest earned, gifts, and winnings
87. After deductions are subtracted
88. $37,000
89. After taxes are calculated, credits are subtracted from taxes owed.
90. No, only for up to $147,000
91. $4,813
92. $1,600