J · 2021年01月29日
NO.PZ2018062016000006
问题如下：
Lucy believes that after retirement she will need about $2 million totally for her daily expenses. At present, she has $1million investment at a stated annual interest rate of 2.5%. Assuming compounded daily, how long does it take for Lucy to have enough money for retirement life?
选项：
A.27.73 years
B.28.07 years
C.26.48 years
解释：
A is correct.
EAR=(1+0.025/365)365-1=0.02531
$1million*(1+0.02531)N =$2million, N=27.73 years.
请问这么算为什么不对 答案并不在选项中
星星_品职助教 · 2021年01月29日
同学你好，
首先要强调的这并不是CFA考试的常规算法。考试的时候不要这么计算。
常规的算法是直接按计算器，PV=-1，PMT=0，FV=2，I/Y=2.531（EAR转化后的结果），CPT N=27.73直接迅速得到答案A
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你的过程我检查了一遍，前两行的公式列式没有问题。
你的计算最终结果和答案差的非常少，应该是在第三行计算时，产生了四舍五入的问题，积累到最后就查了一点点。
如果把第二行的算式用计算器一次性按出来：
先按“1+0.025/365”，按“=”，然后按“LN”，然后按“1/X”，然后“×”，“2，“LN”，然后“/365”，最后按“=”，就可以得到27.7268。这样一步到位，就避免了四舍五入的误差。
但以上这种算法仅做讨论之用，考试的时候还是直接用一排五个键来做吧，快多了。
J · 2021年01月30日
谢谢您。 那在什么时候我们需要转化为EAR呢？ 是在“ stated annual interest rate” 中“ stated"这个关键字吗
星星_品职助教 · 2021年01月30日
@J 回复追问：
1）如果题干中给的描述是stated annual rate XX%，compounding XXX （e.g. stated annual rate of 2.5%， compounded daily）这种形式，就一定要转化。stated annual rate不能直接拿来用。
2）利率转化为多久的利率要看其他题干的信息。I/Y对应的期限要和PMT和N三者一致。假设题目中给出来的N是天数，PMT是每日PMT，这个时候就需要将利率转化为日利率，I/Y=2.5/365. 此时不需要转化成EAR，否则期间就不一致了。
由于本题中选项要求的N是多少年，所以这个时候就可以把利率转化为（有效）年利率，本题中PMT=0可以不用考虑。这样CPT N得出的结果直接就是选项中的多少年。
所以要分题目要求什么，和题干信息来判断究竟应该转化成期间利率还是年利率。
NO.PZ2018062016000006 问题如下 Lubelieves thafter retirement she will neeabout $2 million totally for her ily expenses. present, she h$1million investment a stateannuinterest rate of 2.5%. Assuming compounily, how long es it take for Luto have enough money for retirement life? A.27.73 years B.28.07 years C.26.48 years A is correct.EAR=(1+0.025/365)365-1=0.02531$1million*(1+0.02531)N =$2million, N=27.73 years. EAR为什么是2.531，不是2.5，这里I/Y为什么需要转换
NO.PZ2018062016000006问题如下Lubelieves thafter retirement she will neeabout $2 million totally for her ily expenses. present, she h$1million investment a stateannuinterest rate of 2.5%. Assuming compounily, how long es it take for Luto have enough money for retirement life?A.27.73 yearsB.28.07 yearsC.26.48 yearsA is correct.EAR=(1+0.025/365)365-1=0.02531$1million*(1+0.02531)N =$2million, N=27.73 years.求问怎么用金融计算器计算～
NO.PZ2018062016000006问题如下 Lubelieves thafter retirement she will neeabout $2 million totally for her ily expenses. present, she h$1million investment a stateannuinterest rate of 2.5%. Assuming compounily, how long es it take for Luto have enough money for retirement life?A.27.73 yearsB.28.07 yearsC.26.48 yearsA is correct.EAR=(1+0.025/365)365-1=0.02531$1million*(1+0.02531)N =$2million, N=27.73 years.请问这题能用试错法计算吗，如果能的话要怎么算，谢谢
NO.PZ2018062016000006 问题如下 Lubelieves thafter retirement she will neeabout $2 million totally for her ily expenses. present, she h$1million investment a stateannuinterest rate of 2.5%. Assuming compounily, how long es it take for Luto have enough money for retirement life? A.27.73 years B.28.07 years C.26.48 years A is correct.EAR=(1+0.025/365)365-1=0.02531$1million*(1+0.02531)N =$2million, N=27.73 years. 为什么FV是-1不是1呢？
NO.PZ2018062016000006 问题如下 Lubelieves thafter retirement she will neeabout $2 million totally for her ily expenses. present, she h$1million investment a stateannuinterest rate of 2.5%. Assuming compounily, how long es it take for Luto have enough money for retirement life? A.27.73 years B.28.07 years C.26.48 years A is correct.EAR=(1+0.025/365)365-1=0.02531$1million*(1+0.02531)N =$2million, N=27.73 years. 同题目，这题我代入FV=2, PV=-1,I/Y=2.5,PMT=0，最后算出来的就是28.07，请问这个思路为什么错了呢？
