Ex $8.$ You intend to purchase a $8-$year, $$1000$ face value bond that has a coupon rate of $11\%$ and pays interest annually. The yield on the bond is $10$ percent now and it is expected to remain the constant over its life.

a$)$ Calculate the price of the bond today.

b$)$ What will be the price of the bond one year from today $(P_1)?$

c$)$ What will be the price of bond five years from today $(P_5)?$