Final answer:
The initial sum of money needed is $1813.33.
Step-by-step explanation:
To find the initial sum of money, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the known values:
3698.46 = P(1 + 0.094/2)^(2*9)
Solving for P, the sum of money is $1813.33.