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Janet1106 · 2019年11月24日

问一道题: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.

这道题直接采用250000*(1+3%/365)^(365*n)=1000000,该如何用计算器点击算出n?

还有就是给出的答案算法,没有看懂

1 个答案

星星_品职助教 · 2020年03月08日

同学你好,

如果用你的公式,计算器无法直接求解,只能把答案的月份转化成年后往里面代数一个个试。不过这道题不建议那么做,可以换种方式直接按计算器。

PV=-250000, I/Y=3/365,PMT=0,FV=1000000, CPT N,得到N=16868天后再换算成16868/365=46.21年,即555个月。

答案解释的思路和这个类似,但是答案是先算出来EAR,所以I/Y里面代入的是年利率而不是日利率,最后算出来的N也就直接是46.21年。但这种方法不如直接I/Y代入日利率便捷。可以根据自己的习惯,任选一种解法。加油

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