$4\mathrm{.}32.$ The table below gives Treasury zero rates and cash flows on a Treasury bond. Zero rates are continuously compounded.

$($a$)$ What is the bond's theoretical price?

$($b$)$ What is the bond's yield assuming it sells for its theoretical price?

$\backslash$table$[[$Maturity $($years$),$Zero rate,Coupon payment,Principal$],[0\mathrm{.}5,2\mathrm{.}0\%,$$$20,],[1\mathrm{.}0,2\mathrm{.}3\%,$$$20,],[1\mathrm{.}5,2\mathrm{.}7\%,$$$20,],[2\mathrm{.}0,3\mathrm{.}2\%,$$$20,$$$1,000$