Final answer:
The effective annual rate (EAR) for a nominal rate of 9.00% compounded monthly is approximately 9.38%. This is calculated using the formula EAR = (1 + r/n)^n - 1. The correct answer is c. 9.38.
Step-by-step explanation:
The student asked for the calculation of the effective annual rate (EAR) when the nominal rate is 9.00% compounded monthly. To calculate the EAR, we use the formula EAR = (1 + r/n)n - 1, where r is the nominal annual interest rate and n is the number of compounding periods per year. Substituting the given values into the formula, we have EAR = (1 + 0.09/12)12 - 1. Calculating this gives us the EAR, which is approximately 9.38%. Based on this calculation, the correct answer to the student's question is c. 9.38. It's important to know how to compute the EAR because it reflects the actual yearly return on an investment or cost of a loan when compounding occurs more frequently than once per year. This concept is used in various financial calculations, including determining the amount of money needed for savings goals or loan repayments, as outlined in some interest compounding scenarios provided. For example, to know how much money to deposit in a bank account today to have a certain amount in the future, considering a compound interest rate, you’d reverse-engineer the EAR calculation to find the present value.