Adada · 2021年08月04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%)
比如说8.8% compounded semiannually, 那么1年的stated annual interest rate和EAR分别为多少呢？
星星_品职助教 · 2021年08月04日
同学你好，
stated annual interest rate只是名义上的年化利率，并不代表把钱存进去一年就能拿这么多利息。所以计算器的I/Y键里永远都不会输入stated annual interest rate。
8.0% compounded semiannually中的stated annual interest rate是8.0%
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EAR中的“E”代表Effective，是有效年利率，这是一年实际可以拿到的利息，EAR需要通过公式进行计算。
8.0% compounded semiannually中EAR=（1+8%/2）^2 -1=8.16%，此时计算器的I/Y键输入的是8.16.
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%
