010****0328 · 2021年02月12日
NO.PZ2018062016000010
问题如下：
Mary has a separate account for her annual savings which has a stated annual rate of 3% and compounding quarterly. At the end of each year, she transfers unequal cash flows into this account. Year 1: $500, Year 2: $800, Year 4: $300, Year 5: $500. How much will Mary save for her account at the end of year 5?
选项：
A. $2246.81
B. $2247.65
C. $2281.00
解释：
B is correct.
星星_品职助教 · 2021年02月12日
同学你好，
stated annual rate不能直接拿来用。
如果题干中给的描述是stated annual rate XX%，compounding XXX （e.g. stated annual rate of 3%， compounded quarterly）这种形式，就一定要转化。
本题中现金流都是年度现金流，所以需要将利率转化为年度利率的形式，即转化成EAR。
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可以理解为stated annual rate是一个“假”的利率。真实的利率是季度利率0.75%。
为了方便不同期限的利率做对比（例如对比季度利率和月利率），就会把各个期限的利率都按单利形式简单做年化。例如月利率年化后的结果就是月利率×12。这个简单年化后的利率就是stated annual rate，本题的stated annual rate=0.75%×4=3%。
由这个过程可以看出，这个3%是简单年化后的结果，而不是1块钱存进去一年后可以真实获得的利率。
而EAR就是实际（effective）年利率，是1块钱存进去一年后可以真实获得的利率，这里面考虑了复利效果。例如在本题中，一块钱存进去是按季度复利的，所以会按照0.75%的年利率复利四次，即EAR=（1+0.75%）^4 -1。从计算逻辑可以看出，这个值（EAR）由于有复利作用，一定要比stated annual rate大。
所以精确计算的时候不能用stated annual rate，要用转化后的利率，在本题中就是EAR。
NO.PZ2018062016000010 问题如下 Mary ha separate account for her annusavings whiha stateannurate of 3% ancompounng quarterly. the enof eayear, she transfers unequcash flows into this account. Ye1: $500, Ye2: $800, Ye3: $0, Ye4: $300, Ye5: $500. How muwill Mary save for her account the enof ye5? A.$2246.81 B.$2247.65 C.$2281.00 B is correct. 用CF计算是不是先求EAR，然后输入每期现金流，输入I/Y，然后cpt NFV
NO.PZ2018062016000010问题如下 Mary ha separate account for her annusavings whiha stateannurate of 3% ancompounng quarterly. the enof eayear, she transfers unequcash flows into this account. Ye1: $500, Ye2: $800, Ye3: $0, Ye4: $300, Ye5: $500. How muwill Mary save for her account the enof ye5? A.$2246.81B.$2247.65C.$2281.00B is correct.请问这个题的计算流程是什么样的，没有理解。要先算什么再算什么？
NO.PZ2018062016000010问题如下 Mary ha separate account for her annusavings whiha stateannurate of 3% ancompounng quarterly. the enof eayear, she transfers unequcash flows into this account. Ye1: $500, Ye2: $800, Ye3: $0, Ye4: $300, Ye5: $500. How muwill Mary save for her account the enof ye5? A.$2246.81B.$2247.65C.$2281.00B is correct.本题的答案是每一年单独计算 最后加上总额，我想问一下为什么不是第一年算出来的金额 加上第二年又存进去的的钱作为第二年的本金，以此类推到第五年
NO.PZ2018062016000010 问题如下 Mary ha separate account for her annusavings whiha stateannurate of 3% ancompounng quarterly. the enof eayear, she transfers unequcash flows into this account. Ye1: $500, Ye2: $800, Ye3: $0, Ye4: $300, Ye5: $500. How muwill Mary save for her account the enof ye5? A.$2246.81 B.$2247.65 C.$2281.00 B is correct. 这道题可不可以用N,IY,PV,PMT,FV这五个一年一年的算呢
NO.PZ2018062016000010问题如下 Mary ha separate account for her annusavings whiha stateannurate of 3% ancompounng quarterly. the enof eayear, she transfers unequcash flows into this account. Ye1: $500, Ye2: $800, Ye3: $0, Ye4: $300, Ye5: $500. How muwill Mary save for her account the enof ye5? A.$2246.81B.$2247.65C.$2281.00B is correct.EAR=3.034% 可以直接视作NPV键里的I（折现率）嘛？怎么感觉哪里怪怪的？
