"Today" is August 24, 2020. Chang wants to buy a $90000 face value bond that has a coupon rate of 6.75% (comp. semi.) and that pays its coupons June 30 and December 31 every year. The bond matures on Dec 30, 2031, and the current interest rate is 5.75% (comp. semi.).

a) What is the amount of each coupon payment?

b) Find the clean price P₀ of the bond on June 30, 2020.

c) Use the ACT/ACT daycount convention to calculate the fraction k of the current coupon period based on "today's" date.

d) Find the dirty price "today" using the linear approximation P = P₀ * (1 + ik). (Where i is the effective 6 month rate and k is the fraction from part c).)

e) Find the dirty price "today" using the compound interest formula P = P₀ * (1 + i)^k. (Where i is the effective 6 month rate and k is the fraction from part c).)