可以解释一下这道题目用的知识点和解析吗，不太明白解析是怎么做的

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:

€1,000,000e^0.03(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

如题

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1 个答案

星星_品职助教 · 2023年07月31日

同学你好，

本题考察不同计息频率下，终值的差异。

对于连续复利而言，只能用公式计算。代入连续复利公式 FV=PV× e的(r×n)次方，可得最终本息和为 1,000,000×e^(3%×4)=1,127,496.85

对于daily compounding部分，计算器按键如下：

PV= -1,000,000； N=365×4； I/Y=3/365； PMT=0； CPT FV=1,127,491.29。

（如果结果有细微差异，则来自于I/Y的四舍五入）

此后两者做差即可。

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NO.PZ2022123001000004 问题如下 Given a €1,000,000 investment for four years with astateannurate of 3%compouncontinuously, the fferenin its interestearnings comparewith the same investment compounily is closest to: A.€1. B.€6. C.€455. With continuous compounng, the investment earns:€1,000,000e0.03(4) – €1,000,000= €1,127,496.85 – €1,000,000= €127,496.85With ily compounng, 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 fferenbetween continuous compounng anily compounng is€127,496.85–€127,491.29 =€5.56, or ≈€6 为什么不是1000000（1+3%）的4次方= FV？

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2023-09-09 04:26 2 · 回答