问一道题：NO.PZ2016082402000002

问题如下：

Lisa Smith, the treasurer of Bank AAA, has $100 million to invest for one year. She has identified three alternative one-year certificates of deposit (CDs), with different compounding periods and annual rates. CD1: monthly, 7.82%; CD2: quarterly, 8.00%; CD3: semiannually, 8.05%; and CD4: continuous, 7.95%. Which CD has the highest effective annual rate (EAR)?

选项：

CD1

CD2

CD3

CD4

解释：

ANSWER: D

A dollar initially invested will grow to CD1 $\;{(1+\frac{7.82\%}{12})}^{12}=1.08107$, CD2:${(1+\frac{8.00\%}4)}^4=1.08243$, CD3:${(1+\frac{8.05\%}2)}^2=1.08212$ , CD4: $e^{7.95\%}=1.08275$. Hence, CD4 gives the highest final amount and EAR.