Question on bonds

Hey guys quick conceptual question - why do bond prices go down with increasing coupon frequency (all else equal)? Consider a 3 year bond paying 9% coupon with FV = 100 and required return = 11%. If the interest is paid annually, the price is $95.11, but if the interest is paid semiannually, the price is $95.

Wouldn’t someone be willing to pay more for a bond that gave more frequent payments, as you would benefit from compounding? Obviously I am missing something simple or thinking about something in the wrong way - any clarity would be appreciated.

The problem is that you’re not using the same effective required return. You’re using 11% for the annual-pay bond but 11.3025% (= 1.0552 − 1) for the semiannual-pay bond.