To determine the interest rate per period when $1 is compounded semiannually for 10 years at an annual interest rate of 8%, we follow these steps:
1. Identify the annual interest rate: The problem states that the annual interest rate is 8%.
2. Determine how many times the interest is compounded per year: Since the interest is compounded semiannually, it means the interest is compounded twice a year.
3. Calculate the interest rate per period: To find the interest rate for each compounding period, divide the annual interest rate by the number of times the interest is compounded per year.
[tex]\[
\text{Interest rate per period} = \frac{\text{Annual interest rate}}{\text{Number of compounding periods per year}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Annual interest rate} = 0.08 \quad (\text{or } 8\%)
\][/tex]
[tex]\[
\text{Number of compounding periods per year} = 2
\][/tex]
[tex]\[
\text{Interest rate per period} = \frac{0.08}{2} = 0.04
\][/tex]
So, the interest rate per period is 0.04, or 4%.
