Question

Bank A pays 4% interest compounded annually on deposits, while Bank B pays 3% compounded daily.

Based on the EAR (or EFF%), which bank should you use?

A. You would choose Bank A because its EAR is higher.
B. You would choose Bank B because its EAR is higher.
C. You would choose Bank A because its nominal interest rate is higher.
D. You would choose Bank B because its nominal interest rate is higher.

Answer 1

Based on the calculations, Bank A offers a higher effective annual rate (EAR) of 4% since Bank B's EAR, although compounded daily, is still less than 4% but higher than its nominal rate of 3%. Therefore, one should choose Bank A.

Step-by-step explanation:

When deciding between two banks with different compounding interest rates, the effective annual rate (EAR) is the determining factor. To compare the banks, we calculate the EAR for each.

The formula for EAR is EAR = (1 + i/n)^(n*k) - 1, where 'i' is the nominal interest rate, 'n' the number of compounding periods per year, and 'k' the number of years.

For Bank A, with 4% compounded annually, the EAR is simply 4% or 0.04 since it's compounded once per year.

For Bank B, with 3% compounded daily, n equals 365. Therefore, EAR = (1 + 0.03/365)^(365*1) - 1. After calculating, EAR for Bank B is slightly higher than 3%.

From this, we can compare the two EARs:

• Bank A EAR = 4%
• Bank B EAR > 3% (but less than 4%)

Choosing Bank A provides a higher EAR, making option A the correct answer.