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.
这个题把 0.03 除以 12 或者除以 365 按月份,天数 求 EAR 都可以得到 555 的正确结果,但是按年度求次方为啥不对:
250000*((1+0.03)^(555/12))=980983
250000*((1+0.03)^(563/12))=1000506
按年算的话是 563 更合理啊