Answer
$9\%$ compounded monthly
Work Step by Step
Case 1. Given $r=0.09$, let $t=1$, we have $A_1=P(1+\frac{0.09}{12})^{12}\approx1.0938P$
Case 2. Given $r=0.088$, let $t=1$, we have $A_2=P(1+\frac{0.088}{365})^{365}\approx1.0920P$
Thus case 1 with $9\%$ compounded monthly is better.
