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Swan陈师雯 · 2021年03月29日

在PV FV计算中是使用有效年利率还是名义利率

  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.

有效年利率是指实际利率吗？

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1 个答案

星星_品职助教 · 2021年03月29日

同学你好，

概念辨析如下：

①有效年利率（effective annual rate）可以理解为1块钱存入银行，存满一年后真实可以获得的利息收益。

②名义上的年利率（stated annual rate）并不是实际可以获得的利率，只是把期间利率单利年化了，便于不同产品间进行粗略对比。stated annual rate必须要做转化。

③PV/FV计算中根据具体的题目情况，可能直接使用期间利率，也可能使用转化后得到的有效年利率（effective annual rate），但永远不会在计算器里输入名义上的年利率（stated annual rate）

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