(1) A bond will mature in 20 years. It has a 5% coupon rate and will pay annual coupons. If the bond has a face value of $1,000 and a 4% yield to maturity, what should be the price of the bond today? What if YTM goes up to 5%? What if YTM goes up to 6%?

(2) What would be the price of the bond above in (1) if the coupons were paid semiannually?

(3) What is the relationship between the coupon rate of a bond and the yield to maturity in terms of the bonds price. In particular, when do we have a discount bond, a par bond, and a premium bond? Please explain the rational behind the relationship as if you are explaining this relationship to a novice of Finance.

(4) Both Bond Tom and Bond Jerry have 4% coupons, make semiannual payments, and have YTM of 3%. Bond Tom has two years to maturity, whereas Bond Jerry has 30 years to maturity. If the interest rates (YTM) suddenly rise by 2 percent point to 5%, what is the percentage change in the price of Bond Tom and Bond Jerry? Based on your answer, what can you say about the relationship between the interest rate risk and the time to maturity?