Corporate Bond A returns $6\mathrm{.}0\%$ of its cost in present value $($PV$)$ terms in Year $1,5\mathrm{.}5\%$ in Year $2,5\mathrm{.}0\%$ in Year $3,4\mathrm{.}5\%$ in Year $4,$ and $79\mathrm{.}0\%$ in Year $5.$ Corporate Bond B returns $4\mathrm{.}0\%$ of its cost in PV terms in Year $1,3\mathrm{.}5\%$ in Year $2,3\mathrm{.}0\%$ in Year $3,2\mathrm{.}5\%$ in Year $4,$ and $87\mathrm{.}0\%$ in Year $5.$ If A and B have the same yield to maturity, which of the following must be true?

Group of answer choices

Bond A is more price sensitive to interest rate changes than Bond B$.$

All of the answer choices are correct.

Bond A has a shorter duration than Bond B$.$

Bond A has a lower PV than Bond B$.$

Bond A has a smaller coupon than Bond B$.$