42. Under what conditions must a distinction be made between money to be received today and money to be received in the future?
42.在什么情况下，必须区分今天要收的钱和将来要收的钱？

A. A period of recession
一个。经济衰退时期

B. When idle money can earn a positive return
B.当闲置资金可以获得正回报时

C. When there is no risk of non payment in the future
C. 当将来没有不付款的风险时

D. When current interest rates are different from expected future rates
D. 当前利率与预期未来利率不同时

43. As the compounding rate becomes lower and lower, the future value of inflows approaches
43. 随着复利率越来越低，未来流入的价值越来越近

A. 0
答：0.

B. the present value of the inflows.
B.流入的现值。

C. infinity
C. 无穷大.

D. More information is needed to answer the question.
D. 需要更多的信息来回答这个问题。

44. Time value of money considers which of the following item(s) that change the value of money?
44. 货币的时间价值考虑以下哪一项会改变货币的价值？

A. Inflation
A. 通货膨胀

B. Interest
B. 利息

C. Currency changes
C. 货币变动

D. All of the options are true
D. 所有选项均为真

45. If you invest $10,000 today at 10% interest, how much will you have in 10 years?
45. 如果您今天以 10% 的利息投资 10,000 美元，10 年后您将拥有多少？

A. $13,860
答：13,860 美元

B. $25,940
B. 25,940美元

C. $3,860
C. 3 860美元

D. $80,712
D. 80 712美元

FV = PV × FV_IF (App. A: 10%, 10 years)
FV = PV × FV _IF （应用。答：10%，10年）

= $10,000 × 2.594 = $25,940
= 10,000 美元 × 2.594 = 25,940 美元

46. In determining the future value of a single amount, one must consider
46. 在确定单一金额的未来价值时，必须考虑

A. the periodic payments at a given interest rate and time.
A. 按给定利率和时间定期付款。

B. the future value at a given interest rate and time.
B.在给定利率和时间下的未来价值。

C. the future periodic payments discounted at a given interest rate and time.
C. 按给定利率和时间贴现的未来定期付款。

D. the present value at a given interest rate and time.
D.在给定利率和时间下的现值。

47. The concept of time value of money is important to financial decision making because
47. 货币时间价值的概念对财务决策很重要，因为

A. it emphasizes earning a return on invested capital.
A.它强调从投资资本中获得回报。

B. it recognizes that earning a return makes $1 today worth less than $1 received in the future.
B. 它认识到，赚取回报使今天的 1 美元价值低于未来收到的 1 美元。

C. it can be applied to future cash flows in order to compare different streams of income.
C.它可以应用于未来的现金流量，以便比较不同的收入流。

D. All of these options are true.
D. 所有这些选项都是正确的。

48. As the discount rate becomes higher and higher, the present value of inflows approaches
48. 随着贴现率越来越高，流入的现值越来越近

A. 0
答：0.

B. minus infinity.
B.减去无穷大。

C. plus infinity.
C.加无穷大。

D. More information is needed.
D. 需要更多的信息。

49. How much must you invest today at 8% interest in order to see your investment grow to $8,000 in 10 years?
49. 您今天必须以 8% 的利息投资多少才能看到您的投资在 10 年内增长到 8,000 美元？

A. $3,070
答：3,070 美元

B. $3,704
B. 3,704美元

C. $3,105
C. 3 105美元

D. $17,272
D. 17 272美元

PV = A × PV_IF (App. B: 8%, 10 periods)
PV = A × PV _IF （约 B：8%，10 个周期）

= $8,000 × 0.463 = $3,704 
= 8,000 美元 × 0.463 = 3,704 美元

50. An annuity may best be defined as
50. 年金最好定义为

A. a payment at a fixed interest rate.
A. 以固定利率付款。

B. a series of payments of unequal amount.
B.一系列金额不等额的付款。

C. a series of yearly payments, regardless of amount.
C.一系列的年度付款，无论金额如何。

D. a series of consecutive payments of equal amounts.
D.一系列等额的连续付款。

51. You are to receive $12,000 at the end of five years. The available yield on investments is 6%. Which table would you use to determine the value of that sum today?
51. 五年后，您将收到 12,000 美元。可用的投资收益率为6%。您今天会使用哪个表来确定该金额的价值？

A. Present value of an annuity of $1
A. 年金为1美元的现值

B. Future value of an annuity of $1
B. 1 美元年金的未来价值

C. Present value of $1
C. 现值1美元

D. Future value of $1
D. 1 美元的未来价值

52. You are to receive $12,000 at the end of each of five years. The available yield on investments is 6%. Which table would you use to determine the value of that sum today?
52. 您将在五年中每年结束时收到 12,000 美元。可用的投资收益率为6%。您今天会使用哪个表来确定该金额的价值？

A. Present value of an annuity of $1
A. 年金为1美元的现值

B. Future value of an annuity of $1
B. 1 美元年金的未来价值

C. Present value of $1
C. 现值1美元

D. Future value of $1
D. 1 美元的未来价值

53. As the interest rate increases, the present value
53. 随着利率的上升，现值

A. increases
A.增加.

B. decreases
B.减少.

C. remains the same.
C.保持不变。

D. Not enough information is given to tell.
D.没有提供足够的信息来说明。

54. As the time period until receipt increases, the present value
54. 随着收货时间的增加，现值

A. decreases
A.减少.

B. remains the same.
B.保持不变。

C. increases
C.增加.

D. Not enough information is given to tell.
D.没有提供足够的信息来说明。

55. A company wants to find the yield on an investment that requires a certain amount today in which then returns a single amount some time in the future. Which time value of money table would the company use?
55. 一家公司希望找到今天需要一定金额的投资的收益率，然后在未来某个时间返回单一金额。公司会使用哪种货币时间价值表？

A. the present value of $1 or the future value of $1.
A. 现值 1 美元或未来价值 1 美元。

B. the future value of an annuity of $1.
B. 年金的未来价值为 1 美元。

C. present value of an annuity of $1.
C. 年金的现值为 1 美元。

D. None of these are correct.
D. 这些都不正确。

56. If a father and mother set aside a certain amount each year for their daughter ’s college fund, which table would be used to determine the amount necessary to be put away each year in order to reach a certain goal once the daughter attends college?
56.如果父亲和母亲每年为女儿的大学基金留出一定数额，那么在女儿上大学后，为了达到某个目标，每年需要存入的金额是多少？

A. The present value of $1
一个。现值 $1

B. The future value of $1.
B.1 美元的未来价值。

C. The future value of an annuity of $1.
C. 年金的未来价值为 1 美元。

D. Present value of an annuity of $1.
D. 年金的现值为 1 美元。

57. Shah sets aside $2,000 each year for five years. After five years, he then withdraws the funds on an equal annual basis for the next four years. If Shah wishes to determine the amount of the annuity to be withdrawn in years 6 through 9, he should use the following two tables in this order:
57. Shah 在五年内每年拨出 2,000 美元。五年后，他在接下来的四年中每年平均提取资金。如果沙阿希望确定在第 6 年至第 9 年提取的年金金额，他应该按以下顺序使用以下两个表格：

A. present value of an annuity of $1; future value of an annuity of $1
A. 年金的现值为 1 美元;年金的未来价值为 1 美元

B. future value of an annuity of $1; present value of an annuity of $1
B. 年金的未来价值为 1 美元;年金的现值为 1 美元

C. future value of an annuity of $1; present value of $1
C. 年金的未来价值为 1 美元;现值为 1 美元

D. future value of an annuity of $1; future value of $1
D. 年金的未来价值为 1 美元;未来价值为 1 美元

58. To save for her newborn son ’s college education, Lea Wilson will invest $1,000 at the end of each year for the next 20 years. The interest rate is 10%. What is the future value?
58. 为了攒钱供刚出生的儿子上大学，莉亚·威尔逊将在未来 20 年内每年年底投资 1,000 美元。利率为10%。未来价值是多少？

A. $8,514
答：8,514美元

B. $2,980
B. 2,980美元

C. $63,440
C. 63 440美元

D. $57,275
D. 57 275美元

FV_A = A × FV_IFA (App. C: 10%, 20 periods)
FV _A = A × FV _IFA （约 C：10%，20 个周期）

= $1,000 × (57.275 ) = $57,275
= 1,000 美元× （57.275 ） = 57,275 美元

59. If you were to put $1,000 in the bank at 6% interest each year for the next 10 years, which table would you use to find the ending balance in your account?
59. 如果您在未来 1,000 年内每年以 6% 的利息将 1,000 美元存入银行，您会使用哪张表来查找您账户的期末余额？

A. Present value of $1
A. 现值为1美元

B. Future value of $1
B. 1 美元的未来价值

C. Present value of an annuity of $1
C. 1美元年金的现值

D. Future value of an annuity of $1
D. 1 美元年金的未来价值

60. If you were to put $1,000 in the bank at 6% interest each year for the next 10 years, how much would you have as an ending balance in your account?
60. 如果您在未来 1,000 年内每年以 6% 的利息将 1,000 美元存入银行，您的账户中有多少期末余额？

A. Present value of $1
A. 现值为1美元

B. Future value of $1
B. 1 美元的未来价值

C. Present value of an annuity of $1
C. 1美元年金的现值

D. Future value of an annuity of $1
D. 1 美元年金的未来价值

61. The interest factor (IF) for the future value of an ordinary annuity is 4.641 at 10% for four years. If we wish to accumulate $8,000 by the end of four years, how much should the annual payments be?
61. 普通年金未来价值的利息系数（IF）为4.641，利率为10%，为期四年。如果我们希望在四年结束时积累 8,000 美元，那么每年的付款应该是多少？

A. $2,500
答：2,500 美元

B. $2,000
B. 2,000美元

C. $1,724
C. 1 724美元

D. $37,128
D. 37 128美元

A $8,000/4.641
A 8,000 美元/4.641

A = $1,724
A = 1,724 美元

62. Mr. Blochirt is creating a college investment fund for his daughter. He will put in $1,000 per year for the next 5 years starting one year from now and expects to earn a 6% annual rate of return. How much money will his daughter have when she starts college?
62. Blochirt 先生正在为他的女儿创建一个大学投资基金。从现在开始的一年，他将在未来 5 年内每年投入 1,000 美元，并期望获得 6% 的年回报率。他的女儿上大学后会有多少钱？

A. $4,212
答：4,212美元

B. $12,263
B. 12 263美元

C. $5,000
C. 5 000美元

D. $5,637
D. 5 637美元

FV_A = A × FV_IFA (App. C: 6%, 5 periods) 
FV _A = A × FV _IFA （约 C：6%，5 个周期）

= $1,000 ×5.637 = $5,637
= 1,000 美元 ×5.637 = 5,637 美元

63. Mr. Nailor invests $5,000 in a money market account at his local bank. He receives annual interest of 8% compounded for four years. How much total return will his investment earn during this time period?
63. Nailor 先生在当地银行的货币市场账户中投资了 5,000 美元。他每年获得 8% 的复利利息，为期四年。在此期间，他的投资将获得多少总回报？

A. $3,675
答：3,675美元

B. $1,800
B. 1,800美元

C. $6,254
C. 6 254美元

D. $8,570
D. 8,570美元

FV = PV × FV_IF (App. A: 8%, 4 periods) 
FV = PV × FV _IF （应用。答：8%，4个周期）

= $5,000 × 1.360 = $6,800 
= 5,000 美元 × 1.360 = 6,800 美元

$6,800 - Initial investment of $5,000 = $1,800
$6,800 - 初始投资 $5,000 = $1,800

64. Lou Lewis borrows $10,000 to be completely repaid over 10 years at 8%. Repayment of principal in the first year is ______.
64. Lou Lewis 借款 10,000 美元，在 10 年内以 8% 的价格全额偿还。第一年偿还本金______。

A. $1,493
答：1,493 美元

B. $693
B. 693 美元

C. $690
C. 690 美元

D. $885
D. 885 美元

A = $10,000/6.710
A = 10,000 美元/6.710 美元

A = $1,493 annual payment less interest in year 1 ($10,000 × 8%) of $800 = $693
A = 1,493 美元的年付款减去第 1 年的利息（10,000 美元× 8%）的 800 美元 = 693 美元

65. Sharon Smith will receive $1 million in 20 years. The discount rate is 10%. As an alternative, she can receive $200,000 today. Which should she choose?
65. 莎朗·史密斯将在 20 年内获得 100 万美元。贴现率为10%。作为替代方案，她今天可以收到 200,000 美元。她应该选择哪个？

A. The $200,000 today.
一个。今天的 200,000 美元。

B. The $1 million in 20 years.
B.20 年内 100 万美元。

C. Both equal the same value.
C. 两者等于相同的值。

D. Neither option would be preferred.
D. 这两种选择都不是可取的。

PV = FV × PV_IF (App. B: 10%, 20 periods)
PV = FV × PV _IF （应用 B：10%，20 个周期）

= ($1,000,000 /(1 + .10)²⁰ = $149,000
= （$1,000,000 /（1 + .10） ²⁰ = $149,000

66. Pedro Gonzalez will invest $5,000 at the end of each year. If the interest rate is 8%, what will the value be after three years?
66. 佩德罗·冈萨雷斯 （Pedro Gonzalez） 将在每年年底投资 5,000 美元。如果利率是8%，三年后的价值是多少？

A. $12,885
A. 12,885 美元

B. $6,300
B. 6,300美元

C. $16,230
C. 16 230美元

D. $15,400
D. 15 400美元

FV_A = A × FV_IFA (App. C: 8%, 3periods)
FV _A = A × FV _IFA （约 C：8%，3 个周期）

= $5,000 × (3.246) = $16,230
= 5,000 美元× （3.246） = 16,230 美元

Topic: Future value-annuity
主题：未来价值年金

67. Ambrin Corp. expects to receive $2,000 at the end of each year for 10 years. Then the corporation expects to receive $3,500 per year for the following 10 years, at the end of each year. What is the approximate present value of this 20-year cash flow? Use an 8% discount rate.
67. Ambrin Corp. 预计在 10 年内每年年底收到 2,000 美元。然后，该公司预计在接下来的 10 年中每年在每年年底收到 3,500 美元。这20年现金流的大致现值是多少？使用 8% 的折扣率。

A. $24,294
A. 24,294 美元

B. $27,870
B. 27 870美元

C. $32,389
C. 32 389美元

D. $2,547
D. 2,547美元

PV_A = A × PV_IFA (App. D: 8%, 10 periods)
PV _A = A × PV _IFA （约 D：8%，10 个周期）

= $2,000 ×6.710 = $13,420
= 2,000 美元 ×6.710 = 13,420 美元

PV_A = A × PV_IFA (App. D: 8%, 10 periods)
PV _A = A × PV _IFA （约 D：8%，10 个周期）

= $3,500 ×6.710 = $23,485× PV_IF (App. B: 8%, 10 periods)
= $3,500 ×6,710 = $23,485×PV _IF （应用 B：8%，10 个周期）

PV_IF = $23,485× (.463) = $10,874
PV _IF = 23,485 美元× （.463） = 10,874 美元

$13,420 + $10,874 = $24,294
13,420 美元 + 10,874 美元 = 24,294 美元

OR

PV_IFA(8%, 20 periods) minus PV_IFA (8%, 10 periods) = PV_IFA years 11 through 20
PV _IFA （8%，20 个周期）减去 PV _IFA （8%，10 个周期）= PV _IFA 第 11 年至 20 年

PLUS PV_IFA (8%, 10 periods)× $2,000
PLUS PV _IFA （8%，10 期）× 2,000 美元

TOTAL of present values of both cash streams
两种现金流的现值合计

68. Fishermen’s Corp. is considering purchasing a boat. If the boat was purchased, it is expected to receive $20,000 at the end of the first year, $40,000 at the end of the second year, and $60,000 at the end of the third year within its business. What is the boat worth to Fishermen’s Corp today, assume an 8% discount rate.
68. 渔民公司正在考虑购买一艘船。如果购买了这艘船，预计第一年年底将获得 20,000 美元，第二年年底将获得 40,000 美元，第三年年底将获得 60,000 美元。今天这艘船对渔民公司的价值是多少，假设 8% 的折扣率。

A. $120,000
答：120,000 美元

B. $100,440
B. 100 440美元

C. $47,640
C. 47 640美元

D. $98,756
D. 98 756美元

Using Present value of $1 table: ($20,000*.926) + ($40,000 * .857) + ($60,000 * .794) = $100,440
使用 $1 表的现值：（$20,000*.926） + （$40,000 * .857） + （$60,000 * .794） = $100,440

69. Dr. J. wants to buy a Dell computer that will cost $3,000 three years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn an 8% annual return. How much should he set aside at the end of each year?
69. J. 博士想买一台戴尔电脑，从今天起三年后将花费 3,000 美元。他希望在每年年底留出相等的数额，以积累所需的数额。他可以获得 8% 的年回报率。每年年底他应该留出多少？

A. $879
答：879 美元

B. $627
B. 627 美元

C. $924
C. 924 美元

D. $9,738
D. 9 738美元

A = $3,000/3.246
A = 3,000 美元/3.246 美元

A = $924
A = 924 美元

70. Mr. Fish wants to build a house in ten years. He estimates that the total cost will be $150,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?
70.鱼先生想在十年内盖房子。他估计总成本为 150,000 美元。如果他可以在每年年底存出 10,000 美元，他必须获得多大的回报率才能获得所需的金额？

A. Between 8% and 10%
A. 在 8% 到 10% 之间

B. Between 6% and 8%
B. 在6%至8%之间

C. Above 10%
C. 10%以上

D. Between 4% and 6%
D. 在4%至6%之间

FV_IFA = FV_A (App. C: 10 periods)/A 
FV _IFA = FV _A （应用 C：10 个周期）/A

FV_IFA = $150,000/10,000 = 15.0 Rate of return = between 8% to 10% on the future value of an annuity table. 
FV _IFA = $150,000/10,000 = 15.0 回报率 = 年金表未来价值的 8% 至 10% 之间。

71. Babe Ruth Jr. has agreed to play for the Cleveland Indians for $3 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?
71. Babe Ruth Jr. 已同意在未来 10 年内以每年 300 万美元的价格为克利夫兰印第安人队效力。你会用什么表格来计算这份合约的价值（以今天的美元计算）？

A. Present value of an annuity
A. 年金的现值

B. Present value of a single amount
B. 单一金额的现值

C. Future value of an annuity
C. 年金的未来价值

D. Future value of a dollar
D. 一美元的未来价值

72. Football player Walter Johnson signs a contract calling for payments of $250,000 per year, which begins 10 years from now and then continue for five more years after that. To find the value of this contract today, which table or tables should you use?
72. 足球运动员沃尔特·约翰逊 （Walter Johnson） 签署了一份合同，要求每年支付 250,000 美元，从现在开始 10 年，然后再持续五年。要查找今天此合约的价值，您应该使用哪张或哪张表？

A. The future value of $1
一个。1 美元的未来价值

B. The future value of an annuity of $1 and the future value of $1
B.年金的未来价值为 1 美元，未来价值为 1 美元

C. The present value of an annuity of $1 and the present value of $1
C. 年金为1美元的现值和现值为1美元

D. The present value of $1 and the future value of $1
D. 1 美元的现值和 1 美元的未来价值

73. Mike Carlson will receive $12,000 a year from the end of the third year to the end of the 12^th year (10 payments). The discount rate is 10%. The present value today of this deferred annuity is ______.
73. 迈克·卡尔森 （Mike Carlson） 从第三年末到 12 ^th 年末（12 次付款）每年将获得 10 美元。贴现率为10%。该递延年金的现值为______。

A. $61,450
答：61,450美元

B. $42,185
B. 42 185美元

C. $60,909
C. 60 909美元

D. $55,379
D. 55 379美元

PV_A = A × PV_IFA (App. D: 10%, 10 periods)
PV _A = A × PV _IFA （约 D：10%，10 个周期）

= $12,000 × 6.145 = $73,740
= 12,000 美元 × 6.145 = 73,740 美元

PV = FV × PV_IF (App. B: 10%, 3 periods)
PV = FV × PV _IF （应用 B：10%，3 个周期）

= $73,740 × .751 = $55,379
= 73,740 美元 × .751 = 55,379 美元

74. The shorter the length of time between a present value and its corresponding future value,
74. 现值与其对应的未来值之间的时间越短，

A. the lower the present value, relative to the future value.
A.相对于未来价值，现值越低。

B. the higher the present value, relative to the future value.
B.相对于未来价值，现值越高。

C. the higher the interest rate used in the discounting to the present value.
C.贴现时使用的利率越高。

D. None of these options are correct.
D. 这些选项都不正确。

75. A dollar today is worth more than a dollar to be received in the future because
75.今天的一美元比将来收到的一美元更有价值，因为

A. a stated rate of return is guaranteed on all investment opportunities.
答：所有投资机会都保证有规定的回报率。

B. the dollar can be invested today and earn interest.
B.美元今天可以投资并赚取利息。

C. inflation will increase the purchasing power of a future dollar.
C.通货膨胀将增加未来美元的购买力。

D. None of these options are true.
D. 这些选项都不是真的。

76. The higher the interest rate used in determining the future value of a $1 annuity,
76. 用于确定 1 美元年金未来价值的利率越高，

A. the smaller the future value at the end of the period.
A.期末未来价值越小。

B. the greater the future value at the end of a period.
B.期末的未来值越大。

C. the greater the present value at the beginning of a period.
C.期初的现值越大。

D. None of these options. The interest has no effect on the future value of an annuity.
D. 这些选项都不是。利息对年金的未来价值没有影响。

77. Mr. Darden is selling his house for $200,000. He bought it for $164,000 ten years ago. What is the annual return on his investment?
77. 达顿先生以 200,000 美元的价格出售他的房子。十年前，他以 164,000 美元的价格买下了它。他的投资年回报率是多少？

A. 2%
答：2%

B. Between 3% and 4%
B. 在3%至4%之间

C. 10%
约10%

D. Less than 1%
D. 少于1%

PV_IF = PV (App. B: 10 periods)/FV
PV _IF = PV（应用 B：10 个周期）/FV

= $164,000/$200,000 = 0.82; Return = 2%
= 164,000 美元/200,000 美元 = 0.82;回报率 = 2%

78. Mr. Bubble wants to sell his bubble machine for $1,000,000, but it might take awhile before it is valued that high. He bought it for $149,000 and is earning annual interest of 10% on the machine. How long will Mr. Bubble have to wait before the machine is valued at $1,000,000?
78. 泡泡先生想以 1,000,000 美元的价格出售他的泡泡机，但可能需要一段时间才能估价那么高。他以 149,000 美元的价格购买了它，并在这台机器上赚取了 10% 的年利息。Bubble 先生要等多久才能将这台机器的价值提高到 1,000,000 美元？

A. 20 years
A. 20年

B. 10 years
B. 10年

C. 5 years
C. 5年

D. More than 20 years
D. 20年以上

= $149,000 / $1,000,000 = .149 on table present value of $1 (future value of $1 table can also be used. Take the .149 factor and find 10% next to 20 years. 20 years is the answer.
= $149,000 / $1,000,000 = .149 表现值为 $1（也可使用 $1 表的未来值。以 .149 因子为例，找到 10 年以下的 20%。20年就是答案。

79. Increasing the number of periods will increase all of the following except
79. 增加周期数将增加以下所有方面，但

A. the present value of an annuity.
A. 年金的现值。

B. the present value of $1.
B. 现值 1 美元。

C. the future value of $1.
C. 1 美元的未来价值。

D. the future value of an annuity.
D. 年金的未来价值。

80. Joe Nautilus has $210,000 and wants to retire. What approximate return must his money earn so he may receive annual benefits of $30,000 for the next 10 years?
80. Joe Nautilus 有 210,000 美元，想退休。他的钱必须赚取多少近似回报，才能在未来 10 年内获得 30,000 美元的年度福利？

A. Greater than 10%
A. 大于 10%

B. Between 8% and 10%
B. 在8%至10%之间

C. Between 6% and 8%
C. 在6%至8%之间

D. Lower than 6%
D. 低于 6%

PV_IFA = PV_A (App. D: 10 periods)/A 
PV _IFA = PV _A （应用 D：10 个周期）/A

= $210,000/$30,000 = 7.0; Return = between 6% and 8%
= 210,000 美元/30,000 美元 = 7.0;回报率 = 介于 6% 和 8% 之间

81. You will deposit $2,000 today. It will grow for five years at 12% interest, but compounded semi-annually. You will then withdraw the funds annually over the next four years at the end of each year, with an annual interest rate of 8%. Your annual withdrawal will be approximately ______.
81. 您今天将存入 2,000 美元。它将以 12% 的利率增长五年，但每半年复利一次。然后，您将在未来四年内每年年底提取资金，年利率为 8%。您的年度提款额约为 ______。

A. $2,340
答：2,340 美元

B. $4,332
B. 4,332美元

C. $797
C. 797 美元

D. $1,082
D. 1,082美元

FV = PV × FV_IF (App. A: 6%, 10 periods)
FV = PV × FV _IF （应用。答：6%，10 个周期） 

= $2,000 × 1.791 = $3,582
= 2,000 美元 × 1.791 = 3,582 美元 

A = PV_A (App. D: 8%, 4 periods) 
A = PV _A （约 D：8%，4 个周期）

PV_IFA= $3,582/3.312 = $1,082
PV _IFA = 3,582 美元/3.312 = 1,082 美元

82. You will deposit $200,000 today. It will grow for five years at 12% interest, but compounded semi-annually. What will your investment grow to?
82. 您今天将存入 200,000 美元。它将以 12% 的利率增长五年，但每半年复利一次。您的投资将增长到什么程度？

A. $111,600
A. 111 600美元

B. $1,120,000
B. 1,120,000美元

C. $352,468
C. 352 468美元

D. $358,200
D. 358 200美元

FV = PV × FV_IF (App. A: 6%, 10 periods)
FV = PV × FV _IF （应用。答：6%，10 个周期）

= $200,000 × 1.791 = $358,200
= 200,000 美元 × 1.791 = 358,200 美元 

83. Carol Thomas will pay out $6,000 at the end of year two and $8,000 at the end of year three. Then Carol will receive $10,000 at the end of year four. With an interest rate of 10%, what is the net value of the payments versus receipts in today's dollars?
83. 卡罗尔·托马斯 （Carol Thomas） 将在第二年结束时支付 6,000 美元，在第三年结束时支付 8,000 美元。然后卡罗尔将在第四年结束时获得 10,000 美元。在利率为 10% 的情况下，以今天的美元计算，付款与收据的净值是多少？

A. $7,326
答：7,326美元

B. $10,242
B. 10 242美元

C. $17,794
C. 17 794美元

D. $4,134
四 134美元

PV = FV × PV_IF (App. B: 10%, 2 periods)
PV = FV × PV _IF （应用 B：10%，2 个周期）

= $6,000 × .826 = $4,956
= 6,000 美元 × .826 = 4,956 美元

PV = FV × PV_IF (App. B: 10%, 3 periods)
PV = FV × PV _IF （应用 B：10%，3 个周期）

= $8,000 × .751 = $6,008
= 8,000 美元 × .751 = 6,008 美元

PV = FV × PV_IF (App. B: 10%, 4 periods)
PV = FV × PV _IF （应用 B：10%，4 个周期）

= $10,000 × .683 = $6,830
= 10,000 美元 × .683 = 6,830 美元

Net Value of Payments = ($4,956) + ($6,008) + $6,830 = $4,134
付款净值 = （$4,956） + （$6,008） + $6,830 = $4,134

84. John Doeber borrowed $150,000 to buy a house. His loan cost was 16% annually because of his bad credit score. He promised to repay the loan in 5 years on a quarterly basis.. How much are the quarterly payments?
84. 约翰·多伯借了 150,000 美元买了房子。由于他的信用评分不佳，他的贷款成本每年为 16%。他承诺在5年内按季度偿还贷款。每季度付款多少？

A. $11,453
A. 11 453美元

B. $45,811
B. 45 811美元

C. $13,113
C. 13 113美元

D. $11,038
D. 11 038美元

PV_A = A × PV_IFA (App. D: 16%/4 = 4%, 5 * 4 = 20 periods) 
PV _A = A × PV _IFA （应用 D：16%/4 = 4%，5 * 4 = 20 个周期）

A = PV_A/PV_IFA = $150,000/13.590 = $11,038
A = PV _A /PV _IFA = 150,000 美元/13.590 = 11,038 美元

85. John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 10 equal annual payments. What is the principal outstanding after the first loan payment?
85. John Doeber 借了 150,000 美元买了房子。他的贷款成本为6%，他承诺每年分10次偿还贷款。第一次还款后未偿还的本金是多少？

A. $143,555
A. 143 555美元

B. $134,560
B. 134 560美元

C. $141,200
C. 141 200美元

D. $138,620
D. 138 620美元

PV_A = A × PV_IFA (App. D: 6%, 10 periods)
PV _A = A × PV _IFA （应用 D：6%，10 个周期）

= $150,000/7.360 = $20,380

Annual Payment - Interest = Amount to be applied to principal
年度还款额 - 利息 = 用于本金的金额

$20,380 - (.06 × $150,000) = $11,380
20,380 美元 - （.06 × 150,000 美元） = 11,380 美元

Outstanding principal at end of year 1 = Loan - Payment to principal 
第 1 年末未偿还本金 = 贷款 - 支付本金

= $150,000 - $11,380

= $138,620

86. John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 10 equal annual payments. What are John’s annual payment amounts?
86. 约翰·杜伯借了 150,000 美元买了房子。他的贷款成本为6%，他承诺每年分10次偿还贷款。Johns 的年付款金额是多少？

A. $15,000
A. 15,000 美元

B. $20,380
B. 20 380美元

C. $15,445
C. 15 445美元

D. $11,453
D. 11 453美元

PV_A = A × PV_IFA (App. D: 6%, 10 periods)
PV _A = A × PV _IFA （应用 D：6%，10 个周期）

= $150,000/7.360 = $20,380

87. A home buyer signed a 20-year, 8% mortgage for $72,500. Given the following information, how much should the annual loan payments be?
87. 一位购房者以 72,500 美元的价格签署了一份为期 20 年、利率为 8% 的抵押贷款。鉴于以下信息，每年的贷款还款额应该是多少？

A. $1,584
答：1,584 美元

B. $7,384
B. 7,384美元

C. $15,555
C. 15 555美元

D. $15,588
D. 15 588美元

$72,500/9.818 = $7,384.

88. A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement, you will have $73,425. The plan anticipates earning 8% interest. Given the following information, how much will you be able to take out on an annual basis while you are retired?
88. 退休计划保证在 20 年内向您或您的遗产支付固定金额。退休时，您将拥有 73,425 美元。该计划预计赚取8%的利息。根据以下信息，您在退休后每年可以取出多少钱？

A. $1,435
答：1,435 美元

B. $13,070
B. 13 070美元

C. $7,479
C. 7 479美元

D. $13,102
D. 13 102美元

$73,425/9.818 = $7,479

89. After 10 years, some shares of stock originally purchased for $500 total were sold for $900 total. What was the yield on the investment? Choose the closest answer.
89. 10 年后，一些最初以 500 美元购买的股票以总计 900 美元的价格出售。投资的收益率是多少？选择最接近的答案。

A. 10%
答：10%

B. 4%

C. 8%
约8%

D. 6%

PVIF = PV/FV (App. B: 10 periods)
PVIF = PV/FV（应用 B：10 个周期）

= $500/$900 = 0.555 Yield = approx 6%
= $500/$900 = 0.555 收益率 = 约 6%

90. Dr. Stein has just invested $10,000 for his son (age 7). The money will be used for his son's education 10 years from now. He calculates that he will need $21,598 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal? Choose the closest answer.
90. Stein 博士刚刚为他的儿子（7 岁）投资了 10,000 美元。这笔钱将在10年后用于儿子的教育。他计算出，当儿子上学时，他将需要 21,598 美元用于儿子的教育。Stein博士需要多大的回报率才能实现这一目标？选择最接近的答案。

A. 10%
答：10%

B. 8%

C. 4%
约4%

D. 1%

PV_IF = PV/FV (App. B: 10 periods)
PV _IF = PV/FV（应用 B：10 个周期）

= $10,000/$21,598 = 0.463 Return: 8%
= $10,000/$21,598 = 0.463 回报：8%

91. The future value of a $500 investment today at 8% annual interest compounded semiannually for five years is ______.
91. 今天以 8% 的年利率和五年的半年复利计算的 500 美元投资的未来价值是______。

A. $805
答：805 美元

B. $814
B. 814 美元

C. $740
C. 740 美元

D. $923
D. 923 美元

FV = PV × FV_IF (App. A: 8%/2=4%, 5*2=10 periods)
FV = PV × FV _IF （应用。答：8%/2=4%，5*2=10个周期）

= $500 × 1.480 = $740
= 500 美元× 1.480 = 740 美元

92. Dan would like to save $1,500,000 by the time he retires in 30 years and believes he can earn an annual return of 8%. How much does he need to invest in each of the following years to achieve his goal?
92. Dan 希望在 1,500,000 年后退休时节省 30 美元，并相信他可以获得 8% 的年回报率。在接下来的几年里，他需要投资多少才能实现他的目标？

A. $13,241
A. 13,241美元

B. $133,239
B. 133 239美元

C. $10,727
C. 10 727美元

D. $52,450
D. 52 450美元

= $1,500,000/113.283 = $13,241

93. Sydney saved $10,000 during her first year of work after college and plans to invest it for her retirement in 20 years. How much will she have available for retirement if she can make 8% on her investment?
93. 悉尼在大学毕业后工作的第一年存了 10,000 美元，并计划在 20 年后为她的退休金投资。如果她能从投资中赚取 8% 的收益，她将有多少退休金？

A. $2,150
答：2,150 美元

B. $457,620
B. 457 620美元

C. $46,610
C. 46 610美元

D. $217,250
D. 217 250美元

FV = PV × PV_IF (8%, 20 periods) = $10,000 ×4.661 = $46,610
FV = PV × PV _IF （8%，20 个周期）= 10,000 美元 ×4.661 = 46,610 美元

94. Luke believes that he can invest $5,000 per year for his retirement in 30 years. How much will he have available for retirement if he can earn 8% on his investment and begins investing one year from now?
94. 卢克认为，他每年可以投资 5,000 美元用于 30 年后的退休生活。如果他能从投资中赚取 8% 并在一年后开始投资，他将有多少可用于退休？

A. $566,400
A. 566 400美元

B. $681,550
B. 681 550美元

C. $150,000
C. 150,000美元

D. $162,000
D. 162 000美元

FV_A = A × FV_IFA (App. C: 8%, 30 periods)
FV _A = A × FV _IFA （约 C：8%，30 个周期）

= $5,000 × 113.28 = $566,400
= 5,000 美元 × 113.28 = 566,400 美元

95. Ian would like to save $2,000,000 by the time he retires in 30 years. If he believes that he can achieve a 6% rate of return, how much does he need to deposit each year, starting one year from now, to achieve his goal?
95. Ian 希望在 2,000,000 年后退休时节省 30 美元。如果他认为自己可以达到6%的回报率，那么从现在开始的一年开始，他每年需要存入多少资金才能实现他的目标？

A. $12,065
答：12,065美元

B. $37,500
B. 37 500美元

C. $5,790
C. 5 790美元

D. $25,298
D. 25 298美元

= $2,000,000/79.058 = $25,298

96. Jeff believes he will need a $60,000 annual income during retirement. If he can achieve a 6% return during retirement and believes he will live 20 years after retirement, how much does he need to save by the time he retires? Assume he'll start drawing his money out one year after his retirement.
96. 杰夫认为他在退休时需要 60,000 美元的年收入。如果他能在退休时获得6%的回报，并相信退休后还能活20年，那么到退休时他需要存多少钱？假设他将在退休一年后开始提取资金。

A. $724,055
A. 724 055美元

B. $1,600,000
B. 1,600,000美元

C. $688,200
C. 688 200美元

D. $209,320
D. 209 320美元

PV_A = A × PV_IFA (App. D: 6%, 20 periods)
PV _A = A × PV _IFA （约 D：6%，20 个周期）

= $60,000 × 11.470 = $688,200
= 60,000 美元 × 11.470 = 688,200 美元

97. If Allison has saved $1,000,000 upon retirement, how much money can she live on each year if she can earn 4% per year and will end with $0 when she expects to die 30 years after retirement?
97. 如果艾莉森在退休时存了 1,000,000 美元，如果她每年能赚 4%，当她预计退休 30 年后去世时，她每年能活多少钱？

A. $40,000
A. 40,000 美元

B. $20,953
B. 20 953美元

C. $17,830
C. 17 830美元

D. $57,830
D. 57 830美元

A = PV_A/PV_IFA (App. D: 4%, 30 periods)
A = PV _A /PV _IFA （约 D：4%，30 个周期）

= $1,000,000/17.292 = $57,830

98. Kathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?
98. Kathy 今天有 50,000 美元要投资，她想确定她通过这项投资在 150,000 年内以 10 美元的价格购买房屋的目标是否现实。她必须获得什么回报才能在10年内买下她的房子？

A. Above 10%
A. 10%以上

B. Between 8% to 10%
B. 在8%至10%之间

C. Exactly 10%
C. 正好 10%

D. Below 8%
D. 8%以下

PV_IF = PV/FV (App. B: 10 periods)
PV _IF = PV/FV（应用 B：10 个周期）

= $50,000/$150,000 = 0.333 Return = above 10%
= $50,000/$150,000 = 0.333 回报 = 10% 以上

99. If Gerry makes a deposit of $1,500 at the end of each quarter for five years, how much will he have at the end of the five years assuming a 12% annual return and quarterly compounding?
99. 如果 Gerry 在五年内每个季度末存入 1,500 美元，假设年回报率为 12%，季度复利，他在五年结束时将有多少存款？

A. $40,305
A. 40 305美元

B. $30,000
B. 30,000美元

C. $108,078
C. 108 078美元

D. $161,220
D. 161 220美元

FV_A = A × FV_IFA (App. C: 3%, 20 periods)
FV _A = A × FV _IFA （约 C：3%，20 个周期）

= $1,500 × 26.870 = $40,305
= 1,500 美元 × 26.870 = 40,305 美元

100. Sara would like to evaluate the performance of her portfolio over the past 10 years. What compound annual rate of return has she achieved if she invested $12,000 ten years ago and now has $25,000?
100. Sara 想评估她过去 10 年的投资组合表现。如果她十年前投资了 12,000 美元，现在拥有 25,000 美元，她实现了什么复合年回报率？

A. Between 4% and 6%
答：在4%至6%之间

B. Above 10%
B. 10%以上

C. Between 8% and 10%
C. 在8%至10%之间

D. Between 6% and 8%
D. 在6%至8%之间

PVIF = PV/FV (App. B: 10 periods)
PVIF = PV/FV（应用 B：10 个周期）

= $12,000/$25,000 = 0.48 Return: between 6% and 8%
= $12,000/$25,000 = 0.48 回报：介于 6% 和 8% 之间

101. Lucas expects to receive a sales bonus of $9,500 one year from now. The process of
101. 卢卡斯预计一年后将获得 9,500 美元的销售奖金。过程

determining how much that bonus is worth today is called:
确定今天的奖金价值称为：

A. aggregating. B. discounting.
A.聚合。B.折扣。

C. simplifying. D. compounding.
C.简化。D.复合。

102. Rob wants to invest $25,000 for 7 years. Which one of the following rates will provide him
102. Rob 想投资 25,000 美元，为期 7 年。以下哪一项费率将为他提供

with the largest future value?
具有最大的未来价值？

A. 3 percent simple interest B. 3 percent interest, compounded annually
A. 3% 单利 B. 3% 的利息，每年复利

C. 4 percent simple interest D. 4 percent interest, compounded annually
C. 4% 单利 D. 4% 利息，每年复利

103. You just won $30,00 and deposited your winnings into an account that pays 3.9 percent
103. 您刚刚赢得了 30,00 美元并将您的奖金存入一个支付 3.9% 的账户

interest, compounded annually. How long will you have to wait until your winnings are worth
利息，每年复利。您需要等待多长时间才能获得奖金

$75,00?(使用EXCEL 中的NPER函数计算)

A. 21.24 years B. 25.00 years
A. 21.24 年 B. 25.00 年

C. 22.29 years D. 23.95 years
C. 22.29 年 D. 23.95 年

104. You have $1000 today and want to triple your money in 6 years. What interest rate must you
104. 你今天有 1000 美元，想在 6 年内将你的钱翻三倍。你必须采取什么利率

earn if the interest is compounded annually?（使用EXCEL 中的RATE函数计算）
如果利息每年复利，则赚取？（使用EXCEL中的RATE函数计算）

A. 18.08 percent B. 19.90 percent
A. 18.08% B. 19.90%

C. 20.09 percent D. 21.21 percent
C. 20.09% D. 21.21%

105. Jeanette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the
105. 珍妮特计划在第 1 年结束时节省 600 美元，在第 2 年结束时节省 800 美元，在

end of Year 3. If she earns 3.4 percent on her savings, how much money will she have at the end
三年级结束。如果她的积蓄赚了3.4%，她最后会有多少钱

of Year 3?
三年级？

A. $2,400.00 B. $2,238.47
A. 2,400.00 美元 B. 2,238.47 美元

C. $2,468.69 D. $2,309.16
C. 2,468.69 美元 D. 2,309.16 美元

106. The Jones Brothers recently established a trust fund that will provide annual scholarships of
106. 琼斯兄弟最近设立了一个信托基金，每年提供奖学金

$12,000 indefinitely. These annual scholarships are:
无限期 12,000 美元。这些年度奖学金是：

A. an ordinary annuity. B. an annuity due.
A. 普通年金。B. 到期的年金。

C. amortized payments. D. a perpetuity
C. 摊销付款。D. 永久.

107. S&S Furniture is offering a bedroom suite for $3,200. The credit terms are 60 months at $55
107. S&S Furniture 以 3,200 美元的价格提供卧室套房。信用期限为 60 个月，为 55 美元

per month. What is the interest rate on this offer? （使用EXCEL 中的RATE函数计算）
每月。此优惠的利率是多少？（使用EXCEL 中的RATE函数计算）

A. 1.22 percent B. 1.50 percent
A. 1.22% B. 1.50%

C. 1.65 percent D. 1.15 percent
C. 1.65% D. 1.15%

108. You just received a loan offer from Friendly Loans. The company is offering you $5,0000 at 9.3
108. 您刚刚收到 Friendly Loans 的贷款报价。该公司以 5,0000 的价格为您提供 9.3 美元

percent interest. The monthly payment is only $1000. If you accept this offer, how long will it take
利息百分比。每月付款仅为 1000 美元。如果您接受此优惠，需要多长时间

you to pay off the loan? (使用EXCEL 中的NPER函数计算)

A. 5.84 years B. 5.29 years
A. 5.84 年 B. 5.29 年

C. 6.80 years D. 6.33 years
C. 6.80 年 D. 6.33 年