The Better Deal Is . . .

First, let's get organized. Your principle is $200.00.
For Bank #1 the rate is 9% and the time is half of a year. This means the the interest for the first half of the year will be:

$200.00 x .09 x .50 = $9.00.

After six months you will have $209.00.
Now we need to find out how much you will have at the end of one year.
Your rate and time stay the same, but now your principle is $209.00. The interest for the second half of the year will be:

$209.00 x .09 x .50 = $9.41.

After one year you will have $218.41 in your savings account at Bank #1.
 
 

Now let's find out how much you will have at the end of one year at Bank #2.
Your principle is still $200.00, but now the rate is 9.3% and the time is 1 year. The interest after one year will be:

$200.00 x .093 x 1= $18.60.

After one year you will have $218.60 in your bank account.

Since $218.60 is more than $218.41, you should open a savings account at Bank#2.