There are two bonds. Both bonds have a $$1,000$ face and mature $5$ years from today. Bond

A pays a $3\%$ annual coupon and Bond B pays a $4\%$ annual coupon. Bond A sells for

$$915\mathrm{.}99$ and Bond B for $$960\mathrm{.}14.$ Answer the following:

$($a$)$ What is $r_5?$

$($b$)$ What is $q_5?$