开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

米其林 · 2021年06月02日

这道题为什么要算EAR呀？这个知识点没太懂

  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:

No.PZ2017092702000019 (选择题)

来源: 原版书

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:

添加评论
1 个答案
已采纳答案

星星_品职助教 · 2021年06月02日

同学你好，

这道题在“separate savings account”里面投资的利率是“...at a stated annual interest rate of 2% compounded monthly”.

所有stated annual rate都不能直接用，需要根据计息频率做转化。

（总结一下，凡是看到“..stated annual rate+compounded....”这种组合就需要结合起来根据题目要求做转化）

由于I/Y，N和PMT这三者必须一致，这道题的N是4年，PMT是每年20,000×3.5%=700，所以I/Y转化为年利率（EAR）比较方便。

根据EAR的公式：

（1+2%/12）^12=1+EAR，得到EAR=2.0184%。

所以计算过程如下：

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。选择B选项，细微差异源自计算过程中的四舍五入。

  • 1

    回答

  • 0

    关注

  • 1002

    浏览
相关问题

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

2023-07-12 21:06 1 · 回答

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

2023-05-13 08:06 1 · 回答

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？

2023-05-04 18:35 1 · 回答

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

2023-04-24 21:32 1 · 回答

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。

2023-04-23 22:21 1 · 回答