An investment pays 9 percent interest compounded semi-annually. What is the effective annual interest rate?
To find the effective annual interest rate (EAR) of an investment that pays a stated interest rate compounded semi-annually, we can use the formula:
EAR = (1 + (r/n))^n - 1
Where:
- r is the stated interest rate (as a decimal)
- n is the number of compounding periods per year
In this case, the stated interest rate is 9 percent, which is equivalent to 0.09 as a decimal. The investment compounds semi-annually, so there are two compounding periods per year.
Plugging in these values into the formula, we get:
EAR = (1 + (0.09/2))^2 - 1
Simplifying further:
EAR = (1 + 0.045)^2 - 1
Calculating:
EAR = (1.045)^2 - 1
EAR = 1.092025 - 1
EAR = 0.092025 or 9.2025%
Therefore, the effective annual interest rate for the investment is approximately 9.2025%.