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.
请问下老师什么时后出现state rate 的时候需要转换成EAR来算呢?什么时候不用呢?我自己觉得是compound daily/monthly/quarterly/semiannually 的时候需要转换,但似乎有时候做到类似自字眼的题又不需要转换,直接用state rate就行,有些疑惑,请老师解下疑,谢谢!