To find the annual interest rate, we can use the formula:
simple interest = (principal x rate x time) / 100
where principal is the initial amount, rate is the annual interest rate, and time is the time period in years.
We know that the principal is $100, the simple interest is $3, and the time period is 6 months, which is half a year.
So, we can plug in these values and solve for the annual interest rate:
$3 = ($100 x rate x 0.5) / 100
$3 = $0.5 x rate
rate = $3 / $0.5
rate = 6
Therefore, the annual interest rate is 6%.