题目
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.
答案
B
解析
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)「huixue_img/importSubject/1564548691967217664.png」With daily compounding, the investment earns:「huixue_img/importSubject/1564548692055298048.png」
方法一：连续复利和每日复利的差是： €127,496.85–€127,491.29 =€5.56, or≈€6，相关计算如下所示。 连续复利情况下，投资收益（PV表示的是现值）： PV*e^(rs*N) = €1,000,000*e^(0.03*4) – €1,000,000= €1,127,496.85 – €1,000,000= €127,496.85 以日计息，这个投资的收益为: €1,000,000*(1 0.03/365)^ (365*4) – €1,000,000 = €1,127,491.29 – €1,000,000 = €127,491.29. 方法二(注意不要保留小数带入，直接计算结果带入第三排键)： PV=1,000,000，N=365*4，I/Y=3/365，PMT=0，CPT FV=-1,127,491.29 PV=1,000,000，N=4，I/Y=( e^3%-1)*100，PMT=0，CPT FV=-1,127,496.85