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勇往直前 · 2021年12月06日

CD FV

  1. CFA I
  2. Quantitative

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）

请问老师为什么CD在未来提取时，不算它的FV?谢谢
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1 个答案

星星_品职助教 · 2021年12月06日

同学你好，

我理解你提问的应该是“.....certificate of deposit (CD) that annually pays interest of 3.5%”中产生的：20,000×3.5%=700.

由于这700是每年末都付，一共付4次。也就是等距（每年），等金额（4个都是700）的现金流，所以这是年金中PMT的概念。最后一笔700是PMT中的一部分，并不是FV。

只有未来单独的一笔现金流才可以认为是FV，例如债券每年付利息（coupon），最后到期日统一还本金（principal），这个每年付的利息就是PMT（包括最后一笔利息），而这个单独出来的本金是FV。

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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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