Final answer:
The effective annual rate of interest for an 8% nominal rate compounded semi-annually is calculated using the EAR formula. The result of this calculation is 8.16%, which represents the actual percentage representing the compounded interest over a year.
Step-by-step explanation:
To calculate the effective annual rate (EAR) of interest for a nominal rate of 8% compounded half-yearly, we will use the formula for converting nominal rates to effective rates. This formula takes into account the frequency of compounding periods within the year. Given that the nominal rate (also referred to as the stated or annual percentage rate) is 8%, and it is compounded semi-annually (twice per year), we can calculate the EAR as follows:
- Divide the nominal annual interest rate by the number of compounding periods per year. In our case, 8% divided by 2 periods per year gives us 4% per period.
- Add 1 to the result of the first step. So, we have 1 + 0.04 = 1.04.
- Raise the result to the power of the number of compounding periods per year. So, we need to calculate 1.042, which equals 1.0816.
- Subtract 1 from the result of step 3 to find the EAR. This gives us 1.0816 - 1 = 0.0816 or 8.16%.
Therefore, the effective annual rate of interest corresponding to a nominal rate of 8% per annum payable half-yearly is 8.16%.