Final answer:
The effective interest rate per quarter for an account with 9% interest compounded monthly is approximately 2.247%. This is calculated using the formula for effective interest rate with the values of 9% annual rate, monthly compounding, and quarterly assessment.
Step-by-step explanation:
To compute the effective interest rate per quarter for a savings account that earns 9% interest compounded monthly, we must understand that the effective interest rate measures the amount of interest actually earned based on compounding during a specific time period. In this case, the nominal annual interest rate is 9%, but since the interest is compounded monthly, the actual interest gained over a quarter will be different. The formula for the effective interest rate per period when compounding is more frequent than the period is (1 + i/n)^(n*t) - 1, where i is the nominal annual rate, n is the number of compounding periods per year, and t is the number of periods the money is invested for.
In this scenario, i = 0.09 (9%), n = 12 (monthly compounding), and t = 1/4 (since there are four quarters in a year). Plugging these values into the formula, we calculate the effective interest rate per quarter as follows:
(1 + 0.09/12)^(12*(1/4)) - 1 = (1 + 0.0075)^(3) - 1 = (1.0075)^3 - 1 ≈ 0.0224727 or 2.247%. Therefore, the effective interest rate per quarter is approximately 2.247%.
Comparing to simple interest and other types of compound interest that might be expressed annually or at different frequencies, effective interest rates, especially when compounded more frequently like monthly, are critical to accurately understand the true earning potential of any investment.