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wmm93512 · 2022年04月29日

这里的20000不应该是现值么?

NO.PZ2017092702000019

问题如下:

A client invests €20,000 in a four-year certificate of deposit (CD) that annually pays interest of 3.5%. The annual CD interest payments are automatically reinvested in a separate savings account at a stated annual interest rate of 2% compounded monthly. At maturity, the value of the combined asset is closest to:

选项:

A.

€21,670.

B.

€22,890.

C.

€22,950.

解释:

B is correct,

as the following cash flows show:

The four annual interest payments are based on the CD’s 3.5% annual rate. The first payment grows at 2.0% compounded monthly for three years (where FV is future value): FVN = €700(1 +0.02/12 )3×12 FVN = 743.25 The second payment grows at 2.0% compounded monthly for two years: FVN = 700(1 +0.02/2 )2×12 FVN = 728.54 The third payment grows at 2.0% compounded monthly for one year: FVN = 700(1 +0.02/12 )1×12 FVN=714.13

The fourth payment is paid at the end of Year 4. Its future value is €700. The sum of all future value payments is as follows:

根据EAR的公式:(1+2%/12)^12=1+EAR,得到EAR=2.0184%。

然后:

1. 首先按照年金的方式来计算利息再投资的终值:N=4,I/Y=2.0184,PV=0,PMT=700,CPT FV=-2885.9208;其中700是20,000每年按照3.5%产生的利息,I/Y是转化的EAR,因为利息(PMT)的频率也是一年一付的。

2. 然后把期初的这20,000再加回去,得到22,885.92。(和选项B有写出入是因为四舍五入的问题,但不影响选出答案)

这里的20000不应该是现值么?

1 个答案
已采纳答案

星星_品职助教 · 2022年04月29日

同学你好,

题干中说明了要把这20,000的利息拿出来再投资:“The annual CD interest payments are automatically reinvested in a separate savings account ....”

所以要计算的是再投资的利息情况,此时PV为0,只有固定的每年产生的20,000×3.5%=700的利息作为PMT。

而原始的20,000是一直不变的,最终计算时加回去就行。

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NO.PZ2017092702000019问题如下A client invests €20,000 in a four-yecertificate of posit (C thannually pays interest of 3.5%. The annuinterest payments are automatically reinvestein a separate savings account a stateannuinterest rate of 2% compounmonthly. maturity, the value of the combineasset is closest to:A.€21,670.B.€22,890.C.€22,950. B is correct, the following cash flows show:The four annuinterest payments are baseon the Cs 3.5% annurate. The first payment grows 2.0% compounmonthly for three years (where FV is future value): FVN = €700(1 +0.02/12 )3×12 FVN = 743.25 The seconpayment grows 2.0% compounmonthly for two years: FVN = €700(1 +0.02/12 )2×12 FVN = 728.54 The thirpayment grows 2.0% compounmonthly for one year: FVN = €700(1 +0.02/12 )1×12 FVN=714.13The fourth payment is paithe enof Ye4. Its future value is €700. The sum of all future value payments is follows:根据EAR的公式(1+2%/12)^12=1+EAR,得到EAR=2.0184%。然后1. 首先按照年金的方式来计算利息再投资的终值N=4,I/Y=2.0184,PV=0,PMT=700,CPT FV=-2885.9208;其中700是20,000每年按照3.5%产生的利息,I/Y是转化的EAR,因为利息(PMT)的频率也是一年一付的。2. 然后把期初的这20,000再加回去,得到22,885.92。(和B有写出入是因为四舍五入的问题,但不影响选出答案) 老师,2/12这个不是把月计的利率转成年计吗,和E的区别在哪?谢谢

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