$2\mathrm{.}3$ Transaction Capital Limited issues two bonds with $20-$year maturities. Both bonds are callable at R$1050.$ The first bond is issued at a deep discount with a coupon rate of $4\%$ and a price of R$580$ to yield $8\mathrm{.}4\%.$ The second bond is issued at par value with a coupon rate of $8\mathrm{.}75\%.$

a$)$ What is the yield to maturity of the par bond?

b$)$ If you expect rates to fall substantially in the next two years, which bond would you prefer to hold?