Today is 1 July 2019. Sanjay plan to purchase a corporate bond with a coupon rate of j2 = 3.6% p.a. and face value of 1000 today. This corporate bond matures at par. The maturity date is 1 January 2025. The yield rate is assumed to be j2 = 3.5% p.a. Assume that this corporate bond has a 4.5% chance of default in the first six-month period (i.e., from 1 July 2019 to 31 December 2019), a 4% chance of default in the second six-month period (i.e., from 1 January 2019 to 30 June 2020) and has a 3.5% chance of default in any six-month period during the rest of term of the bond (i.e., from 1 July 2020 to 1 January 2025). Further assume that, if default occurs, Sanjay will receive no further payments at all. Calculate the purchase price for 1 unit of this corporate bond. Round your answer to three decimal places.

a. Carefully draw a contingent cash flow diagram that models this corporate bond from Sanjay’s perspective.

b. Calculate probability probabilities of this corporate bond being nondefault on 1 January 2020, 1 July 2020, 1 January 2021 and 1 July 2021. Round your answer to five decimal places.

c. Calculate the purchase price for 1 unit of this corporate bond. Round your answer to three decimal places.