A bond having a face value of $ $1,000,$ a coupon rate of $10\%$ and a maturity of $10$ years is issued by XYZ Corporation.

$($a$)$ Immediately after the issue the market interest rate falls to $7\%.$ What is the market value of the bond now? Is it a discount, premium or par value bond?

$($b$)$ If you can purchase the bond for $1,500$ what would be the Yield to Maturity of the bond?