1. Consider the following zero coupon curve:
Maturity (years) Zero Coupon Rate (%)
1 4.00
2 4.50
3 4.75
4 4.90
5 5.00
i. What is the price of a 5-year bond with a face value of Ksh 1 million, offering an annual coupon rate of 5%? (6 points)
ii. What is the yield to maturity of this bond? (6 points)
iii. Suppose the zero coupon curve increases instantly and uniformly by 0.5%. What is the new price and the new yield to maturity of the bond? What is the impact of this rate increase for the bondholder?
IV. Now suppose that the zero coupon curve remains stable over time. You have the bond until its expiration. What is the annual rate of return on your investment? Why is this rate different from YTM? 

2. You have bought a bond for Ksh973,020. The bond has a coupon rate of 6.4%, pays interest annually, has a face value of Ksh1 million, 4 years to maturity, and a yield to maturity of 7.2%. The duration of the bond is 3.6481 years. Expect interest rates to drop 0.3% later today.
i. Use the modified duration to find the approximate percentage change in the price of the bond. Find the new price of the bond from this calculation.
ii. Use your calculator to do regular present value calculations to find the new price of the bond at its new yield to maturity.
iii. What is the amount of the difference between the two answers?
Why are your answers different? Explain