What is the effective annual rate (EAR) of a 6\% annual percentage rate (APR) compounded daily? (Assume 365 days in a year.)

• A. 6.18\%
• B. 6.12\%
• C. 6.00\%
• D. 6.25\%

Answer: (A)

Verified step by step guidance

1. Understand the concept: The Effective Annual Rate (EAR) accounts for compounding within a year, unlike the Annual Percentage Rate (APR), which does not. EAR is calculated using the formula: EAR = (1 + r/n)^(n) - 1, where r is the APR as a decimal, and n is the number of compounding periods per year.
2. Convert the APR to a decimal: Since the APR is given as 6%, divide it by 100 to express it as a decimal. This gives r = 0.06.
3. Determine the number of compounding periods per year: Since the interest is compounded daily, there are 365 compounding periods in a year. Thus, n = 365.
4. Substitute the values into the EAR formula: Replace r with 0.06 and n with 365 in the formula EAR = (1 + r/n)^(n) - 1. The formula becomes EAR = (1 + 0.06/365)^(365) - 1.
5. Simplify the expression: Calculate the value inside the parentheses (1 + 0.06/365), raise it to the power of 365, and subtract 1 to find the EAR. This will give the effective annual rate.