问题如下图：
选项：
A. 
B. 
C. 
解释：
星星_品职助教 · 2019年10月12日
同学你好，
这道题目有一个利息再投资的问题。CD产品只是一个载体，在权益里会具体学一些性质。但是实质其实就是本金一个利率投资，利息另一个利率投资。20,000的本金投资后，每年会产生700的本金（20,000*3.5%）。如果是传统年金问题的话，这700也会按照3.5%进行再投资（也就是“利滚利”的复利思想），这种情况直接按计算器就行。但是在这道题目里，这700并不是按照3.5%进行再投资，而是按照2%的名义利率进行再投资的。
这其实是一个符合现实的操作，因为实务中投资收益往往难以按照原投资利率进行再投资。举个例子，比如买了个50万起买的按年付息5%的三年期理财产品，每年末可以获得50万*5%=2.5万的利息，但由于这2.5万不满足50万的起买金额，所以就无法再度购买理财产品并按照5%的利率投资了，可能只能买3%货币市场基金。这个其实就是之后要学的再投资风险的概念。利息无法按照原利率进行再投资也是学到固收知识点时，YTM的缺陷之一，同时也是公司金融中IRR假设的缺陷之一。等学到对应知识点后可以进行关联。
此外这里还有一个陷阱，就是给的再投资利率2%是按月付息的，所以先要转化为EAR=(1+2%/12)^12。
所以这道题要求终值的话，画出时间轴，第一笔700的利息按照EAR投资相当于滚了3年，也就是变成743.25，第二笔700的利息滚了2年，为728.54，第三笔700的利息相当于只再投资了1年，变成714.13，N=4的时候，还有两笔现金流分别是第四笔利息700和本金20,000。加总即可。
加油
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
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） 这道题第一年的利息是700， 第二年的不应该是20700*0.035 = 724.5吗？这样的话，每一年的PMT就不是固定的700了。这个地方没太搞懂，希望老师解析一下，谢谢
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） 我理解可以将利息的再投资作为年金来计算，但是我算的时候我直接使用的I/Y是2%/12因为是以一个月为期复利的，为什么不能用这个作为I/Y而是需要算它的EAR在带入计算器去算？
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） 这题为什么不是把前三笔700求他们的FV PMT=700 PV=0 I/Y=2%/12 n=3*12 求FV 之后加20000+700 为啥这样不对呢
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） 如题。