The effective rate is calculated in the following way:
[tex]r = {(1 + \frac{i}{n} )}^{n} - 1[/tex]
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers:
[tex]r = {(1 + \frac{8\%}{2}) }^{2} - 1 \\ r = {(1 + \frac{1}{25}) }^{2} - 1 \\ r = \frac{676}{625} - 1 \\ r = 0.0816 \: or \: 8.16\%[/tex]
