NO.PZ2017092702000007
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.
根据不同的计息频率来计算两个利息。第一个是“.... compounded continuously”，第二个是“ compounded daily”，分别计算出利息后做差即可。
第一步 计算 按天复利
计算器： R=3/365=0.08219， N=365*4=1460 ，PV=1，000，000 ，计算器求的FV=1，127，491.292
第二步 计算连续复利
计算器 R= e0.03 -1=0.030455 N=4，PV=1，000，000 ，计算器求的FV=1，127，498.891
但是按照EAR的计算
连续复利： 100000*（ e0.03⋅4 -1）=1，127，496.8516
按天复利： 100000* (1+3650.03 ） 365⋅4 =1，127，491.292
所以是不能按照FV公式用计算器计算是吗？或者连续复利怎么计算F V
