第四章答案翻译1-41题

1，如果你现在投资1000美元，年利率为10％，而且你20年内不动用这笔资金，20年后你将拥有多少钱？

FV＝1000×（1＋10％）20

2．

3．

4．

5．

B．12 x $88.85 - $1,000 = $66.20

6．

注意：

A．当计算每个月的比率时不要四舍五入利率，否则你将得不到相同的答案，i＝16/12

B．你必须用相反的公式输入PMT和FV。

C．你必须用相反的公式输入PMT和FV。

7．

8．

9．

10．

假如你首先要支付2个百分点的货币，也就是说，银行只给你98000

美元，那么这笔抵押贷款的真实APR我们计算：

i =0.89575% 每个月。。APR = 12 ? .89575 → 10.75%

$500 x (1.07) = $535

$500 x (1.06) = $530

a.你将决定把钱存在A银行里,因为在年末的时候可以得到更多的钱.这个决定

可以使你多得到5美元.即增值为1%.由于利息每年只增加一次而且这笔钱放在银行帐户里只有一年时间,这个增值一定是因为这1%的利率差别.

b.大多数人都会选择A银行.最终B银行会不得不提高存款利率.但是,很可能A银行支付一个

高利率是为了吸引更多的储蓄者,尽管对银行而言这个利率是不盈利的. A银行最终会为了盈利而将利率降到与B银行同样的利率水平.

13.a.根据72法则72: n = 72/10 = 7.2.所以苏的这笔资金要想在年利率为10%增长到5,000大约要花7.2年.

$2,500 x (1.10)n = $5,000

由于(1.10)n = 2.0

n log 1.10 = log 2.0

n =0.301/0.0414= 7.27 Years

14.计算公式: $20,000 x 1.07 x 1.06 x 1.05 = $23,818.20

15.a.实际年利率:A银行=8%.D银行= [1 +0.075/365]365 - 1 = .07788 = 7.788%

根据实际年利率,你将会选择A银行,因为这样可以获得更多的利息收入.

b.如果A银行8%的年利率要求将钱存一年,你必须确定在这一年中将不需要这笔钱.如果不能确定什末时候需要这笔钱,将钱存在D银行将会更安全.当你随时需要这笔钱的而取出的时候将会造成潜在的利息损失.

FV (A银行) = $1,000 x 1.08 = $1,080

FV (D银行) = $1,000 x 1.07788 = $1,077.88

利息损失=$2.12.

16.实际年利率(EFF)= [1 + APR/m] m– 1

a.(1 + 0.12/12)12 - 1 =0.1268 = 12.68%

b. (1 + 0..10/1)- 1 = 0.10 = 10%

c. (1 + 0.06/365)365 - 1 =0.0618 = 6.18%

EAR=(1.029302)-1=12.25%

18.

PV = $2,500/(1.04)= $2,311.39

PV = $2,500/(1.045)= $2,289.32

通过计算你将会选择在乙银行进行储蓄,因为从现在开始你只需要存入比在甲银行少的现金就可以实现两年后2,500美元的目标.

PV = $2,500/(1.04)= $2,222.49

PV = $2,500/(1.045)= $2,190.74

通过计算你将会选择在乙银行进行储蓄,因为从现在开始你只需要存入比在甲银行少的现金就可以实现两年后2,500美元的目标.

19.

a.大叔给的礼物的终值就是一年后她将收到的$1000.她将得不到任何的利息,因为她只能在一年后才可以得到这笔钱.

b.大姨给的礼物的终值: $900 x (1.12) = $1,008.

c.她将选择大姨给的礼物,因为从现在开始一年后这份礼物的终值将是$1008.大叔给的礼物的终值是$1,000.大姨的礼物可以使她在一年后多得到$8.

d.如果她能仅以10%利率进行投资,那末投资的将来值只有$990: $900 x (1.10) = $990.所以她会选择一年后的$1,000.当利率为11.11%时,两种选择对她来说是一样的: $1000/ (1+i) = $900或者(1+i) = 1,000/900 i = 0.1111 = 11.11%

20.

a.由于另一个投资项目的利率为4%,理性的选择是将工程的现金流以4%的贴现率进行贴现.因为4%的贴现率可以看作是投资的机会成本.所以也是资金的机会成本.

b.项目现金流的现值: PV = $1,000/(1.04)= $961.54

投资项目的净现值: $961.54 - $950 (cost) = $11.54

由于净现值是确定的所以应该投资这个项目.

c.如果银行将其一年期存单的利率提高到5.5%,现值变为: PV = $1,000/(1.055) = $947.87

现在净现值是负的: $947.87 - $950 = - $2.13.所以你不会投资这个项目.

d.当银行一年期的存单利率为5.26%时,两个投资项目对你来说是一样的: $1,000/(1+i) = $950

i = 5.26%

21.题中给出了好几个现金流，我们可以依次把它们代入公式中从而得出答案！

相加就等出净现值：

$6193.47-$2000=$4193.47 (因为英文中没数据，这数据是我自己算的，和英文

中最后的答案有点偏差，不好意思)

(1+i)5 = $1,200 /$995

方程两边同时开五次方：1+i=1.0382

=>i=0.0382=3.82%

做决策时还需要知道当地银行的利率

b).知道银行的利率是3.5%时,你应该建议你堂妹买债券,因为债券的回报率是

3.82%,比银行的利率3.5%高.

c).如果银行的利率是5%,则你会建议你堂妹把钱存入银行中,因为这样她可以得到更高的回报率.

$300 x (1.06)n = $500

(1.06)n = 1.6667

n log 1.06 = log 1.6667

n =log1.6667/log1.06= 8.77

你会选择储蓄公债,因为它可以使你在4年后就得到$500,而选择现金$300的话,你要超过8年才可以得到$500.

$300.在上面的表格中,当利率分别为6%和10%时,NPV时正的,此时,选择债券,当利率为15%时,NPV为负值,所以此时要选择现金$300. 这种NPV分析得到的结果和上面分析得到的结果是一样的.

24. a).要知道年利率,你首先要知道和实际年利率8%相吻合的月利率,然后再拿它乘以12.

1.08 = (1+ i)12

两边同时开12次方得:

1.006434 = 1+ i

i = 0.006434 =0 .6434%

APR=12*0.6434%=7.72%

b).这种方法是先计算这三笔借款得现值,然后再计算具有同一现值分36个月返还的年金.

25). a)(.备注:根据英文答案,题中所说的”和最后一年”要去掉,就只是”第三年要支付$11000”.下面是按照修改后的题做的!!!!!!!!)

贴现率为10%时:

NPV=$5000/1.10+$4000/1.102-$11000/1.103=$-413.22

b).不会采纳该项目.(它有负的净现值NPV)

同样的结果)

这是一个现金流由正变为负的项目,性质就好比是一项负债.IRR=13.6%就好像是债务的利率,当资本的贴现率是10%时你去借一笔利率为13.6%的债务当然使不明智的!所以,应该拒绝该项目!!

26). 用财务计算机可以很快算出几种现金流的净现值:

27). 普通年金的计算公式为:FV=PMT[(1+i)n-1]/i

把题中所给的数据一次代进去就可以得出答案!

或者用财务计算器,可以很快地得出答案:

e).普通年金地的现值的计算公式是:PV=PMT[1-(1+i)-n]/i

把数据代入就可以得到答案.

用财务计算器可以很快得出答案:

f).现值和终值的关系为: FV = PV * (1+i)n

28). 由题知,三年后你要连续7年支付一定的年金,而这种年金是即时年金,用财务计算器可以很快得出答案:

29). a).普通年金的现值计算公式为: PV=PMT[1-(1+i)-n]/i 把数据代进去得出答案.

增加一笔立刻得到的$100,就是在原有现值的基础上加上$100,最后的现值

为:$432.95+$100=$532.95

b).普通年金的终值计算公式为FV=PMT[(1+i)n-1]/I,将数据代入就可以得出答案.

增加一笔立刻得到的$100,这$100在5年后的值为:$100*1.05=$127.63,所以最后的终值为:$552.56+$127.63=$680.19

30). 因为两种选择的的偿还时间是一样的,所以,可以通过比较它们的月偿付款来决定要选择哪一个!用财务计算器可以很快的得出下表:

通过上表的比较你会选择第一种方式买车即按$2000的价格,4%的APR,分三年偿还.因为它的月偿付额要少一点!

31.用NPV净值法，APR=2.9时，三年期按月还清则N=3*12=36.所以可以得到：

$1,998.25

32.有题意可知：N＝1时，有$475.48进入户头，一年后在利率为0.1的情况下他将增值为$523.03,此时取出$150,资金剩373.03。而后此动作不断重复，可得下表：

还有一种比较直接的方法：你去算一下475.48他4年后的FV,在算毅下每年存入150他4年后的FV.你会惊奇地发现它们的值时相等的。

33.由题意知利润的值为5000000。我们知道年盈利率为0.1。可知PV*0.1=5000000所以可以计算出PV＝$50,000,000

你所能承受的最高价也就是你没有超额利润的情况下，那么你最高可能支付PV=50000000

此时你的红利收益率＝5000000/50000000=0.1=10%

34.题目的个人分析：你若直接拿1000000那么你在利率为0.095的情况下也可以每年拿到等量的利息，现在如果你采取了另一种方案，那么你现在就可以得到100000，并且以后每年你都可以继续得到这个数字。那么当你一年后拿到100000时你可以以0.095的利率推算出他现在的资本进应为100000/0.095=1,052,632.在加

在现在马上能拿到的100000。所以两种奖品的差额为100000+1052632＝1152632。如果资金不是急用可以考虑法分期支付。

35.

由计算公式得：

a.$1,000 x (1.07)10 = $1,967.15

b.$1,000 x (1.035)20 = $1,989.79

c.$1,000 x (1.0058)120 = $2,009.66

d.$1,000 x (1.0019178)3650 = $2,013.62

e.$1,000 x e.07x10 = $2,013.75

36．桑米以每月百分之1.5的利息率借入一笔1000美元的贷款，并通过每月50美元的分期方式进行偿还。我们可以计算出分期偿还计划表从而得知12个月后

EFF = [1 + .09]- 1 = .0938 = 9.38%

38．

39．

A. 我可以将这笔钱投资于美元，并在一年后获得1070美元的回报。也可以将这笔钱更换成英镑（666.67）进行投资并在一年后获得726.67英镑。当汇率变换成1.4美元兑换1英镑时，投资于英镑的获利就是1017美元，这比投资于美元是时获利少，所以我会选择投资于美元。

B. 要使一年后两种投资的获利平衡，那么到时的利率就应当是$1.07/.726667或者$1.4725 每英镑，加入一年后的利率是该平衡利率，那么投资于美元依然是更好的选择。40．用实际利率换算之后，普通国库券的预期回报是(7% - 4%)/1.04 = 2.885%，这要比TIPS的3.5%回报率低，换一种方法来说，TIPS给予了更高的名义利息回报（035 +.04 + .035x.04 = .0764 or 7.64%），这要比普通国库券高。

41．计算方法为以下公式：

FV={（1+i）n-1}/i *PMT 或者PV={1-（1+i）-n}/i*PMT

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