On January $1,2022,$ you bought a three$-$year, annual$-$pay coupon bond with a $6\%$

coupon rate, $$1000$ face value, and yield to maturity of $6\%.$ On January $1,2023,$ you

received the first coupon of the bond, and on January $1,2024,$ you receive the second

coupon. Immediately after receiving the second coupon, you sell the bond. Assume

that yields on bonds of all maturities are equal to $4\mathrm{.}5\%$ on January $1,2024.$

$($a$)$ What is the price you paid for the bond on January $1,2022?(2$ points$)$

$($b$)$ What is the selling price of the bond on January $1,2024?(2$ points$)$