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🌊Yuri🌊 · 2023年09月09日

NO.PZ2022123001000004

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:

With continuous compounding, the investment earns:

€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.

The difference between continuous compounding and daily compounding is

€127,496.85–€127,491.29 =€5.56, or ≈€6

为什么不是1000000(1+3%)的4次方= FV?

2 个答案

星星_品职助教 · 2023年09月13日

@🌊Yuri🌊

这个式子不成立,题干中说明“ compounded daily”,所以不能直接使用3%。只能使用:

1)直接用日利率为3%/365

2)用EAR的公式转化为:EAR=(1+3%/365)^365 -1,此后通过1000000(1+EAR)^4= FV来得到FV。

星星_品职助教 · 2023年09月10日

同学你好,

本题题干说明“compounded daily”,所以需要按照日和实际利率来算,不能按年和stated annual rate of 3%来算。