问题如下图：
选项：
A. 
B. 
C. 
解释：
这题用计算器：n＝4×12 pmt＝700/12 pv＝0 I/Y＝2/12 算出FV＝22917. 38 再加上原始的20000，为啥不对呢？
星星_品职助教 · 2019年12月04日
同学你好，
这道题不能直接算一个统一的FV，因为并不是每个700都滚了4年。可以参照答案解析中的时间轴，第一个700的利息实际滚了3年（36个月），第二个700滚了2年（24个月），第三个700滚了1年（12个月），第四个700直接就是终值，不需要复利。
所以这道题是需要解出3个700各自所对应的FV的，不复杂，但是麻烦，考试的时候慢慢做就能做对，加油~
Luka · 2020年03月05日
我现在有点分不清什么时候能算统一的fv什么时候不能了😂
星星_品职助教 · 2020年03月05日
两个角度思考： 1. 这个700是逐年进入账户的，所以可以单独求每一个700的FV，这个就是不统一算。2. 可以把700理解成一个每年进入的PMT，这样先算出来EAR，然后把N也设成多少年，这样就可以算一个统一的FV。
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。