How much money should be deposited today in an account that earns 5 % compounded semiannually so that it will accumulate to $ 10,000 in three years?

The formula for this is: A=P(1+r/n)^(nt)
A = amount in the account
P = amount you start with
r = rate it is compounded
t = time (in years)
n = number of times per year

Since you are looking for the principle, you solve for P
P = (10,000)/(1+(0.05/2))^(2)(3)
P = $8622.97