How are you going to calculate the interest? Will it be once a year just adding 9% of the balance? Will it be monthly (as you seem to refer to this at some point) and if monthly will that be 1/12 of 9%, or the 12th root of (1+9%) (the latter allows for compound interest which will work out at 9%pa, whereas the former will give you more than 9% over the year)?
If it's just once a year adding 9% to the balance, then the calculation is just
balance = balance * (1+annualInterestRate)
so for example a balance of 1000 becomes 1000*(1+0.09) = 1090.
But where did you get the following figures from, and how was 1093.8 calculated?
The amount invested: 1000
Annual interest rate: 9%
Years Future Value