Which of the following bank accounts has the lowest effective annual return?
A) an account that pays 8% nominal interest with daily (365-day) compounding.
B) an account that pays 8% nominal interest with monthly compounding.
C) an account that pays 8% nominal interest with annual compounding.
D) an account that pays 7% nominal interest with daily (365-day) compounding.
E) an account that pays 7% nominal interest with monthly compounding.

Question

Quizplus · Accepted Answer

By inspection, we can see that c must have a lower EFF% than either a or b because they all pay the same nominal rate but c is compounded least frequently. Similarly, d and e pay the same rate, but e is compounded less frequently, hence e must have the lower EFF%. So, the correct answer must be either c or e. It is not obvious which of these two has the lower EFF%, so we must do a quick calculation to determine the correct response. As the following calculations show, e is the correct answer.
 a. $ \quad 8.328 \%=(1+0.08 / 365)^{365-1} $
b. $ \quad 8.300 \%=(1+0.08 / 12)^{12-1} $
c. $ \quad 8.000 \%=(1+0.08 / 1)^{1-1} $
d. $ \quad 7.250 \%=(1+0.07 / 365)^{365-1} $
e. $ \quad7.229 \%=(1+0.07 / 12)^{12-1} $

Which of the Following Bank Accounts Has the Lowest Effective