Answer
$9\%$ compounded quarterly
Work Step by Step
1. For $9\%$ compounded quarterly for one year, we have $A_1=P(1+\frac{0.09}{4})^4\approx1.0931P$
2.For $9\frac{1}{4}\%$ compounded annually for one year, we have $A_2=P(1+\frac{0.0925}{1})=1.0925P$
3. Thus $9\%$ compounded quarterly is better.