Problem 1 (30 points): Lucky Star Inc. just issued a bond with the following characteristics:

Maturity = 3 years

Coupon rate = 8%

Face value = $1,000

YTM = 10%

Interest is paid annually and the bond is noncallable.

a. Calculate the bond's Macaulay duration (10 points) Round "Present value" to 2 decimal places and "Duration" to 4 decimal place.

b. Calculate the bond's modified duration (5 points)

c. Assuming the bond's YTM goes from 10% to 9.5%, calculate an estimate of the price change without considering convexity (5 points).

d. Calculate the convexity of the bond.