188****7003 · 2021年02月17日
NO.PZ2017092702000011
问题如下：
An investment of €500,000 today that grows to €800,000 after six years has a stated annual interest rate closest to:
选项：
A.7.5% compounded continuously.
B.7.7% compounded daily.
C.8.0% compounded semiannually.
解释：
C is correct,
as shown in the following (where FV is future value and PV is present value): If: FVN = PV(1 + rs/m)mN, Then: rs = 0.07988 (rounded to 8.0%)
老师好用公式fv/pv=(1+r/m)m次方的公式算出，为什么是r/2,代入半年计息一次不应该是12么，就是最后一步没看懂
星星_品职助教 · 2021年02月18日
同学你好，
fv/pv=(1+r/m)^m这个公式是用来计算EAR即有效“年”利率的。其中，“r”是stated annual rate，“m”指的是计息频率。
本题C选项中，计息频率是“compounded semiannually”，即每半年计息一次，一年计息2次。所以m=2。
但这道题用的公式实际上是上述公式的一个拓展，即fv/pv=(1+r/m)^（m×N），其中N是按年计息时，一共有多少年。本题中，一共有6年（...after six years...），所以N=6。这是最后一步中2×6=12次方的由来。12是m和N的乘积，但m本身还是等于2的。
所以r/m只能是r/2，不能是r/12.
NO.PZ2017092702000011 问题如下 investment of €500,000 toy thgrows to €800,000 after six years ha stateannuinterest rate closest to: A.7.5% compouncontinuously. B.7.7% compounily. C.8.0% compounsemiannually. C is correct,shown in the following (where FV is future value anPV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×6−1=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2(500,000800,000)2×61−1=2rs rs = 0.07988 (rounto 8.0%) 所以这一题直接用公式算或者用计算器第三排都可以是吗？那这一类型的题到底什么时候用公式什么时候可以用计算器呢？我好懵
NO.PZ2017092702000011 问题如下 investment of €500,000 toy thgrows to €800,000 after six years ha stateannuinterest rate closest to: A.7.5% compouncontinuously. B.7.7% compounily. C.8.0% compounsemiannually. C is correct,shown in the following (where FV is future value anPV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×6−1=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2(500,000800,000)2×61−1=2rs rs = 0.07988 (rounto 8.0%) 请问如果是continuous componng怎么算FV （幂是多少？）
NO.PZ2017092702000011 问题如下 investment of €500,000 toy thgrows to €800,000 after six years ha stateannuinterest rate closest to: A.7.5% compouncontinuously. B.7.7% compounily. C.8.0% compounsemiannually. C is correct,shown in the following (where FV is future value anPV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×6−1=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2(500,000800,000)2×61−1=2rs rs = 0.07988 (rounto 8.0%) 直接带答案的话，500,000六年后变多少
NO.PZ2017092702000011 问题如下 investment of €500,000 toy thgrows to €800,000 after six years ha stateannuinterest rate closest to: A.7.5% compouncontinuously. B.7.7% compounily. C.8.0% compounsemiannually. C is correct,shown in the following (where FV is future value anPV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×6−1=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2(500,000800,000)2×61−1=2rs rs = 0.07988 (rounto 8.0%) 因为每个的利率和期数都不一样，是不是很难算中间那个？所以得每个都算一下？我的计算方法是500,000*（e的7.5次方）=780,000 B 500,000*（1+7.7%/365)的365*6次方=793,500 C 500,000*(1+8%/2)的6*2次方=800，516所以选C.请问我的计算方法对吗？有更简单的答题方法吗？
NO.PZ2017092702000011问题如下investment of €500,000 toy thgrows to €800,000 after six years ha stateannuinterest rate closest to:A.7.5% compouncontinuously.B.7.7% compounily.C.8.0% compounsemiannually.C is correct,shown in the following (where FV is future value anPV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×6−1=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2(500,000800,000)2×61−1=2rs rs = 0.07988 (rounto 8.0%)老师这道题可以用代入，通过计算器第三行算吗？过程PV=-500000FV=800000PMT=0N=2*6 （semi annually）得出IY=3.994（semi annually）又因为是 semi annually所以 annually的rate=3.994*2=7.988 约等于8%
