Question

Gary King borrowed $15,550 from a bank for three years. If the quoted rate (APR) is 7.25 percent, and the compounding is daily, what is the effective annual interest rate (EAR)?

Answer 1

The effective annual interest rate (EAR) for Gary King's loan is approximately 7.3825%.

Step-by-step explanation:

To calculate the effective annual interest rate (EAR), we need to use the formula:

EAR = (1 + i/n)^n - 1

Where i is the quoted rate (APR) as a decimal, and n is the number of compounding periods per year. In this case, the quoted rate is 7.25%, which is 0.0725 as a decimal. Since the compounding is daily, the number of compounding periods per year is 365. Plugging in the values, we get:

EAR = (1 + 0.0725/365)^365 - 1

Simplifying this expression, we find that the effective annual interest rate (EAR) for Gary King's loan is approximately 7.3825%.