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Lee13 · 2023年02月17日

A saver deposits the following amounts in an account paying a stated annual rate of 4%, compounded semiannually: At the end of Year 4, the value of the account is closest to:

NO.PZ2017092702000010

问题如下:

A saver deposits the following amounts in an account paying a stated annual rate of 4%, compounded semiannually:

At the end of Year 4, the value of the account is closest to:

选项:

A.

$30,432

B.

$30,447

C.

$31,677

解释:

B is correct.

To solve for the future value of unequal cash flows, compute the future value of each payment as of Year 4 at the semiannual rate of 2%, and then sum the individual future values, as follows:

根据上表所示,首先计算每笔存款的FV,但是需使用semiannual rate 2%,然后将FV相加求和。

请问可以用现金流的方式在计算器上计算吗?还有公式计算为什么第一年的次方是2*3?每年的复利次数为什么是递减呢?谢谢!

2 个答案

星星_品职助教 · 2023年02月18日

回复提问2&3:

由于计息频率是半年,所以半年的期间利率为4%/2=2%=0.02.

第一年存入的4,000复利到第四年末,经历了三年,所以相当于3×2=6个半年。即4,000以2%的半年期利率一共复利了6次。

同理,第二年存入的8,000复利到第四年末是2×2个半年,以此类推。

星星_品职助教 · 2023年02月18日

同学你好,

回复提问1:

CF功能计算的是(N)PV,本题求的是FV。虽然也能算出,但并不建议用CF功能来算,容易出错。

----

CF算法供参考(不建议使用)

STEP1(求PV):

EAR=4.04%,即I=4.04

CF0=0; C01=4000; C02=8000; C03=7000; C04=10000; F01-F04都是1,直接按向下箭头跳过。I=4.04; CPT NPV=25986.1419

STEP2(从PV转化为FV):

PV=-25986.1419; PMT=0; N=4; I/Y=4.04; CPT FV= 30446.9

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