010****0328 · 2021年02月12日
NO.PZ2018062016000011
问题如下：
To increase current investment value of $25,000 to $35,000 in 5 years, which will be the most appropriate below?
选项：
A. deposit in the account that stated annual rate of 6.55% and compounded continuously
B. deposit in the account that stated annual rate of 7% and compounded monthly
C. deposit in the account that stated annual rate of 6.79% and compounded quarterly
解释：
C is correct. $25,000(1+r/4)4*5=$35,000, r=6.79%.
怎么理解这道题用的这个公式呢 谢谢
星星_品职助教 · 2021年02月12日
同学你好，
以答案解析中的C选项为例，略微变化一下公式的形式，得到：35,000=25,000(1+r/4)^(4*5) ，这个公式的原理相当于讲义上的这个公式：
这个公式是用计算器来解的，由于未知的是stated annual rate， r 或者说r/4，所以是一个求利率I/Y的过程，按键为：
PV=-25,000，FV=35,000，N=4×5=20，PMT=0，CPT I/Y=1.6966. 这时求出的I/Y是季度利率的概念，或者说是r/4的概念。
所以stated annual rate=1.6966×4=6.7864，即stated annual rate≈6.79%。
这个利率和C选项中的“deposit in the account that stated annual rate of 6.79% and compounded quarterly”相符，C选项正确。
A，B选项可以用类似的方法代入。发现求出来的stated annual rate和选项给出的都不相符。可以自己试一下求解~
NO.PZ2018062016000011 问题如下 To increase current investment value of $25,000 to $35,000 in 5 years, whiwill the most appropriate below? A.posit in the account thstateannurate of 6.55% ancompouncontinuously B.posit in the account thstateannurate of 7% ancompounmonthly C.posit in the account thstateannurate of 6.79% ancompounquarterly C is correct. $25,000(1+r/4)4*5=$35,000, r=6.79%. 选B，FV为35440.63 35000，收益更高，所以为什么不选B呢，问题问的是最合适的方式。
NO.PZ2018062016000011 问题如下 To increase current investment value of $25,000 to $35,000 in 5 years, whiwill the most appropriate below? A.posit in the account thstateannurate of 6.55% ancompouncontinuously B.posit in the account thstateannurate of 7% ancompounmonthly C.posit in the account thstateannurate of 6.79% ancompounquarterly C is correct. $25,000(1+r/4)4*5=$35,000, r=6.79%. 如果复利连续计算，用对数算的话，是不是这么算呢？35/25=e的R次方，R=ln(35/25)。
NO.PZ2018062016000011 month=(1+6.96%/12)12次方-1=7.2% quarter=(1+6.96%/4)4次方-1=7.14%
NO.PZ2018062016000011 posit in the account thstateannurate of 7% ancompounmonthly posit in the account thstateannurate of 6.79% ancompounquarterly C is correct. $25,000(1+r/4)4*5=$35,000, r=6.79%.为什么要算成季度？不是年么？
