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安年 · 2020年10月03日

问一道题：NO.PZ2017092702000007 [ CFA I ]

  1. CFA I
  2. Quantitative

问题如下：

Given a €1,000,000 investment for four years with a stated annual rate of 3% compounded continuously, the difference in its interest earnings compared with the same investment compounded daily is closest to:

选项：

A.

€1.

B.

€6.

C.

€455.

解释：

B is correct.

The difference between continuous compounding and daily compounding is

€127,496.85 – €127,491.29 = €5.56, or ≈ €6, as shown in the following calculations. With continuous compounding, the investment earns (where PV is present value) PVersN - PV = €1,000,000e0.03(4) – €1,000,000

= €1,127,496.85 – €1,000,000 = €127,496.85 With daily compounding, the investment earns: €1,000,000(1 + 0.03/365)^365(4) – €1,000,000 = €1,127,491.29 – €1,000,000 = €127,491.29.

请问为什么我算按天复利算出来结果是1127175.66

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2 个答案
已采纳答案

星星_品职助教 · 2020年10月09日

同学你好，

你这个列式没问题，如果直接计算器一次性按出来的话，结果就是1,127,491.292。和答案结果一致。

你这个结果不一致的原因应该是因为分步计算产生了四舍五入，主要是在1+0.03/365 这个地方四舍五入以后，又乘方了1460次方。所以原本很小的差异在很大的乘方后，结果就产生了差异。

可以在输入1+0.03/365后，按“=”，然后不退出计算，直接按“yx”和1460，就不会有问题了。

姿姿不倦 · 2020年12月04日

我也遇到了同样的问题，感谢解答！

星星_品职助教 · 2020年12月04日

加油~

星星_品职助教 · 2020年10月06日

同学你好，

类似的问题可以详细列出你的计算/按键过程，看一下是哪里出的问题

安年 · 2020年10月09日

1,000,000(1 + 0.03/365)^365(4)=1000000*1.000082^1460=1000000*1.127176=1127176，请问这样对吗？

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