Answer
$7678.96$
Work Step by Step
In $A(t)=P(1+\frac{r}{n})^{nt}$ for compound interest $P,r,n,t$ respectively stand for the principal, interest rate per year, the number of times the interest is compounded per year and the number of years. $A(t)=10000$ is the amount after $t$ years. So if we invest $P$ at an interest rate of $r=0.09$ compounded semiannually ($n=2$), the amount after $t=3$ years is:
$10000=P(1+\frac{0.09}{2})^{2(3)}\\P=\frac{10000}{(1+\frac{0.09}{2})^{2(3)}}\approx7678.96$
