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水水 · 2021年05月05日

计算器怎么按？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000006

问题如下：

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:

选项：

A.

555.

B.

563.

C.

576.

解释：

A is correct.

The effective annual rate (EAR) is calculated as follows:

EAR = (1 + Periodic interest rate)m – 1   EAR = (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financial calculator results in (where FV is future value and PV is present value): (1 + 0,030453)N = FVN/PV = ¥1,000,000/¥250,000）So,N = 46.21 years, which multiplied by 12 to convert to months results in 554.5, or ≈ 555 months.

(1 + 0,030453)N= FVN/PV = ¥1,000,000/¥250,000）这个计算器怎么按得出N

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2 个答案

星星_品职助教 · 2021年05月14日

@王水水

回复追问：

题干描述为“....at a stated annual rate of 3% compounded daily”。从做题的角度出发，只要看到stated annual rate和计息频率就需要做转化。

stated annual rate只是一个名义上的利率，所以需要根据计息频率转化为真实利率。而compound daily就是计息频率即每日计息的意思。

这句话的意思就是每天的真实利率是3%/365。

就本题而言，可以直接转化为日利率3%/365来计算，这种情况下“N”也要相应调整为天数。这种计算器按键为PV=-250000， I/Y=3/365，PMT=0，FV=1000000， CPT N，得到N=16868天。然后再换算成16868/365=46.21年，即555个月。

或者转化为EAR=3.045%来计算，这时候算出来的N直接就是年数。如原回复中给出的例子。


星星_品职助教 · 2021年05月05日

同学你好，

不需要考虑公式的形式，除了N以外的所有按键的数据都已经有了，逐个输入即可。

PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年），

然后乘以12得到554.5月

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