Assume Julian has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded continuously. Which account provides the highest effective annual return?
A) Account A
B) Account B
C) Both provide the same effective annual return
D) We don't have sufficient information to make a choice

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) for Account A can be calculated using the formula for compound interest: $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate and $n$ is the number of compounding periods per year. For Account A, this is $EAR_A = (1 + \frac{0.0755}{12})^{12} - 1$, which gives an EAR greater than 7.55%. For Account B, the EAR can be calculated using the formula for continuous compounding: $EAR = e^r - 1$, where $e$ is the base of the natural logarithm (approximately 2.71828), and $r$ is the annual interest rate. For Account B, this is $EAR_B = e^{0.0745} - 1$, which gives an EAR slightly above 7.77%. However, when the calculations are correctly applied, Account A's EAR is actually slightly higher than Account B's EAR when considering the specific rates given and the nature of monthly versus continuous compounding. My explanation mistakenly inverted the conclusion based on the formulas provided. The correct calculation shows that for the rates given, continuous compounding at a slightly lower nominal rate (Account B) can outperform monthly compounding at a slightly higher nominal rate (Account A) in terms of effective annual yield.

Assume Julian Has a Choice Between Two Deposit Accounts