A bond with par value of $$1000$ matures in $15$ years and pays $8\%$ coupon interest annually. The market price of the bonds is $$1085$ and your required rate of return is $10\%$ per year.

a$)$ Compute the yield to maturity from the bond

b$)$ Determine the value of the bond to you given your required rate of return

c$)$ Should you purchase the bond?