2851
description
Transcript of 2851
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Personal Finance: An Integrated Planning Approach, 8e (Frasca) Chapter 2
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The Time Value of Money: All Dollars Are Not Created Equal
1)
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Compounding refers to the A)
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mistake of confusing present values with future values. B)
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process of accumulating value over time. C)
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task of finding a present value. D)
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projection of future payments. Answer :
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B Diff: 1 Topic :
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Interest compounding
2)
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Assuming positive interest rates, a present value of $1,000 A)
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is always more desirable to a future value of $1,000. B)
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is always less desirable than a future value of $1,000. C)
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is no more or no less desirable than a future value of $1,000. D)
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You can't answer without more information. Answer :
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A Diff: 1 Topic :
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Interest compounding
3)
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Given recent market experience a dollar today is worth A)
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more than a dollar five years from now. B)
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less than a dollar five years from now. C)
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about the same as a dollar five years from now. D)
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more or less than a dollar five years from now. Answer :
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A Diff: 1 Topic :
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Economic trends
4)
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You have just put $1,000 in an investment that offers a 12% annual yield, using a simple interest calculation. At the end of two years your interest earned will be
A)
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$120.00. B)
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$144.00. C)
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$240.00. D)
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$254.40. Answer :
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C Diff: 1 Topic :
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Interest compounding
5)
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You have just put $500 in an investment that offers an 8% annual yield, with interest compounded annually. Your total interest earned after two years will be
A)
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$83.20. B)
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$80.00. C)
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$44.60. D)
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$40.00. Answer :
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A Diff: 2 Topic :
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Interest compounding
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6)
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At 12% interest (compounded annually), $20,000 invested today will grow to $________ in three years.
A)
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27,200 B)
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28,099 C)
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31,471 D)
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40,000 Answer :
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B Diff: 1 Topic :
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Future value
7)
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You have just put $5,000 into an investment that offers a 10% annual yield, using a simple interest calculation. At the end of two years your interest earned will be
A)
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$500. B)
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$550. C)
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$1,000. D)
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$1,100. Answer :
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C Diff: 2 Topic :
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Interest compounding
8)
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You have just put $5,000 into an investment that offers a 10% annual yield, with interest compounded annually. Your total interest earned after two years will be
A)
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$550. B)
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$1,000. C)
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$1,050. D)
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$1,100. Answer :
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C Diff: 2 Topic :
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Interest compounding
9)
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The text discusses the topic of compounding over a large number of compounding periods. To illustrate, it shows that $1,000 invested at 8% for 40 years (annual compounding) grows to $21,724. But if you could earn 10% instead of 8%, you would earn ________ more at the end of 40 years.
A)
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$4,431 B)
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25 percent C)
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$23,535 D)
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$1,250 Answer :
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C Diff: 3 Topic :
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Interest compounding
10)
66
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The future value of $12,000 invested today at 6% interest compounded annually for 4 years is
A)
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$23,259. B)
68
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$15,150. C)
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$12,190. D)
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$9,505. Answer :
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B Diff: 1 Topic :
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Future value
73
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11)
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The future value of $5,000 invested today at 3% interest compounded annually for 5 years is
A)
75
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$5,255. B)
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$5,520. C)
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$5,628. D)
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$5,796. Answer :
79
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D Diff: 3 Topic :
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Future value
12)
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You expect a 3% rate of inflation to continue indefinitely into the future. A $10,000 vacation today will cost $________ twenty years from now. (Table or calculator required.)
A)
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10,300 B)
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14,988 C)
84
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18,061 D)
85
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42,944 Answer :
86
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C Diff: 3 Topic :
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Future value
13)
88
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You are deciding whether to start a 40-year retirement investing plan now, or ten years from now. You think rates of return will be about the same in the future as they are now. Discussion in the text of this decision shows
A)
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very little difference in the future value of an investment made now versus one made 10 years from now.
B)
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an investment made now will accumulate about 20% more (at a 10% rate of interest, compounded annually) than the investment made later.
C)
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the same facts as in response b, but the accumulation is only 10% greater. D)
92
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that you will accumulate more in the additional 10 years than you do for the first 30 years. Answer :
93
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D Diff: 2 Topic :
94
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Interest compounding
14)
95
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With an interest rate of 9%, $5,000 will grow to $10,000 in approximately A)
96
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8 years. B)
97
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4 years. C)
98
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12 years. D)
99
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24 years. Answer :
100
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A Diff: 1 Topic :
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Rule of 72
15)
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If you wish to double your money in 6 years, you must earn an interest rate of about A)
103
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8%. B)
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24%. C)
105
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12%. D)
106
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36%. Answer :
107
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C Diff: 1 Topic :
108
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Rule of 72
109
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16)
110
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At an interest rate of 10% it will take approximately how many years to double your investment?
A)
111
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Less than five years B)
112
![Page 113: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/113.jpg)
Between 7 and 8 years C)
113
![Page 114: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/114.jpg)
Between 9 and 10 years D)
114
![Page 115: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/115.jpg)
More than 10 years Answer :
115
![Page 116: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/116.jpg)
B Diff: 1 Topic :
116
![Page 117: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/117.jpg)
Rule of 72
17)
117
![Page 118: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/118.jpg)
An annuity is A)
118
![Page 119: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/119.jpg)
a sum received in the future. B)
119
![Page 120: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/120.jpg)
a sum earned in the future but received now. C)
120
![Page 121: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/121.jpg)
a series of unequal payments. D)
121
![Page 122: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/122.jpg)
a series of equal payments. Answer :
122
![Page 123: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/123.jpg)
D Diff: 1 Topic :
123
![Page 124: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/124.jpg)
Annuities
18)
124
![Page 125: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/125.jpg)
In relation to an ordinary annuity paid in any given year, an annuity due is A)
125
![Page 126: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/126.jpg)
a larger amount. B)
126
![Page 127: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/127.jpg)
a smaller amount. C)
127
![Page 128: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/128.jpg)
an equal amount. D)
128
![Page 129: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/129.jpg)
an unrelated amount. Answer :
129
![Page 130: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/130.jpg)
A Diff: 1 Topic :
130
![Page 131: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/131.jpg)
Annuities
19)
131
![Page 132: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/132.jpg)
The future value of a $500 ordinary annuity received for three years is $________ , assuming an investment rate of 10%:
A)
132
![Page 133: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/133.jpg)
1,655.00 B)
133
![Page 134: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/134.jpg)
665.50 C)
134
![Page 135: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/135.jpg)
1,820.50 D)
135
![Page 136: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/136.jpg)
335.65 Answer :
136
![Page 137: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/137.jpg)
A Diff: 3 Topic :
137
![Page 138: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/138.jpg)
Annuities
20)
138
![Page 139: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/139.jpg)
The future value of a $500 annuity due received for three years is $________, assuming an investment rate of 10%.
A)
139
![Page 140: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/140.jpg)
1,655.00 B)
140
![Page 141: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/141.jpg)
665.50 C)
141
![Page 142: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/142.jpg)
1,820.50 D)
142
![Page 143: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/143.jpg)
335.65 Answer :
143
![Page 144: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/144.jpg)
C Diff: 3 Topic :
144
![Page 145: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/145.jpg)
Annuities
145
![Page 146: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/146.jpg)
21)
146
![Page 147: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/147.jpg)
You will need $228,790 in 28 years to supplement your retirement funds. If you can earn 8% interest, you must save $________ each year. (Table or calculator required.)
A)
147
![Page 148: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/148.jpg)
8,100 B)
148
![Page 149: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/149.jpg)
6,300 C)
149
![Page 150: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/150.jpg)
3,600 D)
150
![Page 151: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/151.jpg)
2,400 Answer :
151
![Page 152: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/152.jpg)
D Diff: 3 Topic :
152
![Page 153: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/153.jpg)
Future value
22)
153
![Page 154: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/154.jpg)
An ordinary annuity assumes ________-of-period payments, while an annuity due assumes ________-of-period payments.
A)
154
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end; beginning B)
155
![Page 156: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/156.jpg)
beginning; end C)
156
![Page 157: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/157.jpg)
end; middle D)
157
![Page 158: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/158.jpg)
beginning; middle Answer :
158
![Page 159: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/159.jpg)
A Diff: 2 Topic :
159
![Page 160: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/160.jpg)
Annuities
23)
160
![Page 161: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/161.jpg)
Assuming a discount rate of 10%, the present value of $1,000 received one year from now is
A)
161
![Page 162: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/162.jpg)
$1,100.00. B)
162
![Page 163: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/163.jpg)
$1,900.00. C)
163
![Page 164: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/164.jpg)
$909.09. D)
164
![Page 165: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/165.jpg)
$990.00. Answer :
165
![Page 166: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/166.jpg)
C Diff: 3 Topic :
166
![Page 167: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/167.jpg)
Present value
24)
167
![Page 168: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/168.jpg)
Assuming a discount rate of 10%, the present value of $1,000 received two years from now is
A)
168
![Page 169: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/169.jpg)
$800.00. B)
169
![Page 170: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/170.jpg)
$826.45. C)
170
![Page 171: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/171.jpg)
$899.90 D)
171
![Page 172: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/172.jpg)
$900.00 Answer :
172
![Page 173: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/173.jpg)
B Diff: 3 Topic :
173
![Page 174: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/174.jpg)
Present value
25)
174
![Page 175: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/175.jpg)
You will buy a lottery ticket. If you win, you have a choice of receiving $995,000 now or three equal end-of-year payments of $400,000. You should take the payments
A)
175
![Page 176: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/176.jpg)
because $1,200,000 is greater than $995,000. B)
176
![Page 177: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/177.jpg)
if you earn 20% or more on your investments. C)
177
![Page 178: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/178.jpg)
if you earn 11% or more on your investments. D)
178
![Page 179: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/179.jpg)
if you earn less than 10% on your investments. Answer :
179
![Page 180: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/180.jpg)
D Diff: 3 Topic :
180
![Page 181: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/181.jpg)
Present value
181
![Page 182: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/182.jpg)
26)
182
![Page 183: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/183.jpg)
An annuity contract will pay you $4,000 a year (end of year) for the next three years. Or, you can choose to receive $12,610 at the end of the third. Assuming that you can earn 8% on investments, you should
A)
183
![Page 184: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/184.jpg)
choose to receive the $4,000 annuity payments. B)
184
![Page 185: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/185.jpg)
choose to receive the $12,610 payment. C)
185
![Page 186: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/186.jpg)
flip a coin to make the choice; each is equally attractive. D)
186
![Page 187: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/187.jpg)
flip a coin to make the choice; each is equally unattractive. Answer :
187
![Page 188: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/188.jpg)
A Diff: 3 Topic :
188
![Page 189: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/189.jpg)
Annuities
27)
189
![Page 190: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/190.jpg)
Which item below is not associated with goal planning? A)
190
![Page 191: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/191.jpg)
Constructing a budget B)
191
![Page 192: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/192.jpg)
Adjusting for inflation C)
192
![Page 193: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/193.jpg)
Making goals concrete D)
193
![Page 194: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/194.jpg)
Determining a savings schedule Answer :
194
![Page 195: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/195.jpg)
A Diff: 1 Topic :
195
![Page 196: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/196.jpg)
Planning
28)
196
![Page 197: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/197.jpg)
Generally speaking, planners can usually seek higher return investments to meet A)
197
![Page 198: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/198.jpg)
short-term goals. B)
198
![Page 199: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/199.jpg)
long-term goals. C)
199
![Page 200: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/200.jpg)
goals of any term. D)
200
![Page 201: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/201.jpg)
dreams, but not goals. Answer :
201
![Page 202: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/202.jpg)
B Diff: 2 Topic :
202
![Page 203: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/203.jpg)
Planning
29)
203
![Page 204: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/204.jpg)
A savings schedule with a zero ending balance means that A)
204
![Page 205: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/205.jpg)
annual deposits are sufficient to meet all goals. B)
205
![Page 206: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/206.jpg)
more savings are needed each year. C)
206
![Page 207: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/207.jpg)
the most desirable schedule has been determined. D)
207
![Page 208: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/208.jpg)
some goals will not be achieved. Answer :
208
![Page 209: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/209.jpg)
A Diff: 2 Topic :
209
![Page 210: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/210.jpg)
Planning
30)
210
![Page 211: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/211.jpg)
Young people most likely prefer a savings schedule with A)
211
![Page 212: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/212.jpg)
a zero ending balance. B)
212
![Page 213: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/213.jpg)
increasing annual deposits. C)
213
![Page 214: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/214.jpg)
decreasing annual deposits. D)
214
![Page 215: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/215.jpg)
negative balances in the early years. Answer :
215
![Page 216: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/216.jpg)
B Diff: 2 Topic :
216
![Page 217: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/217.jpg)
Planning
31)
217
![Page 218: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/218.jpg)
Compounding is the process of increasing present value to future values. Answer :
218
![Page 219: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/219.jpg)
TRUE Diff: 1 Topic :
219
![Page 220: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/220.jpg)
Interest compounding
220
![Page 221: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/221.jpg)
32)
221
![Page 222: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/222.jpg)
Discounting is the process of reducing future values to present values. Answer :
222
![Page 223: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/223.jpg)
TRUE Diff: 1 Topic :
223
![Page 224: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/224.jpg)
Present value
33)
224
![Page 225: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/225.jpg)
The present value of $500 received at the end of each of the next three years is $1,243 (assuming a 10% interest rate).
Answer :
225
![Page 226: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/226.jpg)
TRUE Diff: 2 Topic :
226
![Page 227: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/227.jpg)
Present value
34)
227
![Page 228: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/228.jpg)
You invest $100 today in a two-year certificate of deposit that pays a 10% annual interest rate compounded annually. At maturity, your CD will give you $120.
Answer :
228
![Page 229: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/229.jpg)
FALSE Diff: 1 Topic :
229
![Page 230: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/230.jpg)
Interest compounding
35)
230
![Page 231: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/231.jpg)
A simple interest calculation assumes you reinvest all interest earned in the investment. Answer :
231
![Page 232: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/232.jpg)
FALSE Diff: 1 Topic :
232
![Page 233: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/233.jpg)
Interest compounding
36)
233
![Page 234: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/234.jpg)
Looking at a future value of $1 table, you find the number 4.661 for 20 years and 8%. This means that a dollar invested today will grow to $4.661 at the end of 20 years.
Answer :
234
![Page 235: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/235.jpg)
TRUE Diff: 1 Topic :
235
![Page 236: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/236.jpg)
Future value
37)
236
![Page 237: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/237.jpg)
Compounding is the process of increasing present value to future value. Answer :
237
![Page 238: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/238.jpg)
TRUE Diff: 1 Topic :
238
![Page 239: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/239.jpg)
Interest compounding
38)
239
![Page 240: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/240.jpg)
At an 8% rate, you must invest $5,000 to have $10,000 in about 6 years. Answer :
240
![Page 241: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/241.jpg)
FALSE Diff: 2 Topic :
241
![Page 242: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/242.jpg)
Future value
39)
242
![Page 243: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/243.jpg)
At a 12% interest rate, $2,000 invested today will be worth approximately $8,000 in about 12 years.
Answer :
243
![Page 244: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/244.jpg)
TRUE Diff: 2 Topic :
244
![Page 245: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/245.jpg)
Future value
40)
245
![Page 246: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/246.jpg)
You can double your investment in 6 years if you can earn 12% on your investments. Answer :
246
![Page 247: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/247.jpg)
TRUE Diff: 2 Topic :
247
![Page 248: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/248.jpg)
Rule of 72
41)
248
![Page 249: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/249.jpg)
John cashed in an annuity contract and received $10,000. John bought the contract 24 years ago for $5,000. These amounts indicate a contract rate of approximately 3%.
Answer :
249
![Page 250: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/250.jpg)
TRUE Diff: 3 Topic :
250
![Page 251: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/251.jpg)
Interest compounding
42)
251
![Page 252: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/252.jpg)
The future value of $500 invested at the end of each of the next three years is $1,555 (assuming a 10% interest rate).
Answer :
252
![Page 253: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/253.jpg)
FALSE Diff: 2 Topic :
253
![Page 254: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/254.jpg)
Future value
43)
254
![Page 255: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/255.jpg)
Given identical data, the future value of an ordinary annuity is greater than the future value of an annuity due.
Answer :
255
![Page 256: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/256.jpg)
FALSE Diff: 1 Topic :
256
![Page 257: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/257.jpg)
Annuities
44)
257
![Page 258: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/258.jpg)
If the future value of an ordinary annuity is $8,000, the future value of an annuity due is $7,200 given a 10% interest rate.
Answer :
258
![Page 259: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/259.jpg)
FALSE Diff: 2 Topic :
259
![Page 260: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/260.jpg)
Annuities
45)
260
![Page 261: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/261.jpg)
$500 invested at 8% at the beginning of each of the next four years will grow to approximately $2,433.
Answer :
261
![Page 262: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/262.jpg)
TRUE Diff: 2 Topic :
262
![Page 263: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/263.jpg)
Future value
46)
263
![Page 264: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/264.jpg)
Given identical data, the future value of annuity due is always greater than the future value of an ordinary annuity.
Answer :
264
![Page 265: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/265.jpg)
TRUE Diff: 1 Topic :
265
![Page 266: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/266.jpg)
Annuities
47)
266
![Page 267: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/267.jpg)
At any positive rate of interest, a future value will be greater than a present value. Answer :
267
![Page 268: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/268.jpg)
TRUE Diff: 1 Topic :
268
![Page 269: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/269.jpg)
Interest compounding
48)
269
![Page 270: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/270.jpg)
With a 10% interest rate, the present value of $100 received one year from today is $90.91. Answer :
270
![Page 271: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/271.jpg)
TRUE Diff: 1 Topic :
271
![Page 272: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/272.jpg)
Present value
49)
272
![Page 273: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/273.jpg)
Discounting is the process of reducing future values to present values. Answer :
273
![Page 274: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/274.jpg)
TRUE Diff: 1 Topic :
274
![Page 275: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/275.jpg)
Present value
50)
275
![Page 276: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/276.jpg)
The higher the interest (discount) rate, the greater the present value of a future payment. Answer :
276
![Page 277: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/277.jpg)
FALSE Diff: 1 Topic :
277
![Page 278: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/278.jpg)
Present value
51)
278
![Page 279: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/279.jpg)
Discounting is the reverse process of compounding. Answer :
279
![Page 280: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/280.jpg)
TRUE Diff: 1 Topic :
280
![Page 281: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/281.jpg)
Future value
52)
281
![Page 282: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/282.jpg)
Discounting is the process of reducing future values to present values. Answer :
282
![Page 283: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/283.jpg)
TRUE Diff: 1 Topic :
283
![Page 284: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/284.jpg)
Interest compounding
53)
284
![Page 285: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/285.jpg)
The first step in goal planning is setting up a budget. Answer :
285
![Page 286: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/286.jpg)
FALSE Diff: 1 Topic :
286
![Page 287: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/287.jpg)
Planning
54)
287
![Page 288: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/288.jpg)
An important part of goal planning is adjusting present values for expected inflation. Answer :
288
![Page 289: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/289.jpg)
TRUE Diff: 1 Topic :
289
![Page 290: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/290.jpg)
Planning
55)
290
![Page 291: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/291.jpg)
Making goals concrete begins by determining their costs if they were undertaken today. Answer :
291
![Page 292: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/292.jpg)
TRUE Diff: 1 Topic :
292
![Page 293: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/293.jpg)
Planning
56)
293
![Page 294: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/294.jpg)
Most young people prefer a savings schedule with decreasing annual deposits to the savings account.
Answer :
294
![Page 295: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/295.jpg)
FALSE Diff: 1 Topic :
295
![Page 296: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/296.jpg)
Planning
57)
296
![Page 297: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/297.jpg)
Years with negative balances in the savings schedule implies that loans would be needed to achieve the goals.
Answer :
297
![Page 298: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/298.jpg)
TRUE Diff: 1 Topic :
298
![Page 299: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/299.jpg)
Planning
58)
299
![Page 300: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/300.jpg)
You can earn 10%. If you hope to accumulate $20,000 in 4 years, you must make annual investments (end of period) of $3,918.
Answer :
300
![Page 301: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/301.jpg)
FALSE Diff: 3 Topic :
301
![Page 302: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/302.jpg)
Future value
59)
302
![Page 303: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/303.jpg)
In goal planning, you generally match the savings vehicle to the time when the money is needed; for example, short-range goals are funded with low-risk investments.
Answer :
303
![Page 304: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/304.jpg)
TRUE Diff: 1 Topic :
304
![Page 305: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/305.jpg)
Planning
60)
305
![Page 306: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/306.jpg)
An annual required savings amount confirms our computational accuracy but does not necessarily imply that our savings plan will use that amount each year.
Answer :
306
![Page 307: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/307.jpg)
TRUE Diff: 1 Topic :
307
![Page 308: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/308.jpg)
Planning
61)
308
![Page 309: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/309.jpg)
Ideally, the ending balance in our savings plan is zero. Answer :
309
![Page 310: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/310.jpg)
TRUE Diff: 1 Topic :
310
![Page 311: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/311.jpg)
Planning
62)
311
![Page 312: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/312.jpg)
If actual inflation rates exceed the rates assumed in our goal planning, the required annual savings amount can be reduced.
Answer :
312
![Page 313: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/313.jpg)
FALSE Diff: 1 Topic :
313
![Page 314: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/314.jpg)
Planning
63)
314
![Page 315: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/315.jpg)
Highly volatile inflation rates and earning rates make goal planning a useless activity. Answer :
315
![Page 316: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/316.jpg)
FALSE Diff: 1 Topic :
316
![Page 317: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/317.jpg)
Planning
64)
317
![Page 318: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/318.jpg)
Inflation decreases the purchasing power of money. Answer :
318
![Page 319: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/319.jpg)
TRUE Diff: 1 Topic :
319
![Page 320: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/320.jpg)
Planning
65)
320
![Page 321: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/321.jpg)
Unplanned for inflation makes it easier to reach our financial goals. Answer :
321
![Page 322: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/322.jpg)
FALSE Diff: 1 Topic :
322
![Page 323: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/323.jpg)
Planning
66)
323
![Page 324: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/324.jpg)
Generally, you can invest in higher-return assets for goals that are further out in the future. Answer :
324
![Page 325: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/325.jpg)
TRUE Diff: 1 Topic:
325
![Page 326: 2851](https://reader036.fdocuments.in/reader036/viewer/2022062314/563db7d8550346aa9a8e830f/html5/thumbnails/326.jpg)
Planning
326