Answer
$\approx0.0925$ or $9.25\%$
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. $A(t)$ is the amount after $t$ years.
So if we invest $P=1000$ at an interest rate of $r$ compounded semiannually ($n=2$), the amount after $t=4$ years is: $A=1435.77$
Then our equation is:
$1435.77=1000(1+\frac{r}{2})^{2(4)}\\1.43577=(1+\frac{r}{2})^{2(4)}\\\sqrt[8]{1.43577}=1+0.5r\\r=2(\sqrt[8]{1.43577}-1)\approx0.0925$
or $9.25\%$
