All other things equal, which of the following has the largest price sensitivity to the same percentage point change in interest rates $($largest modified duration$)?$

A $20$ year bond with a $10\%$ coupon yielding $10\%$

A $20$ year bond with a $10\%$ coupon yielding $11\%$

A $20$ year zero coupon bond yielding $11\%$

A $20$ year zero coupon bond yielding $10\%$