A government is issuing a 5 year 15% bond with face amount 1,000,000,000. the perception in the investment community is that the government is unstable, and it is forecast that there is a 10% cahnce that the government will default on their interest payment be the first or second years, a 20% chance of default by the third or fourth years, and a 25% chance of default (on the interest and principal) by the fifth year. All probabilities are uncunditional(measured form time 0, so that, for instance, the probability that the 7th coupon will be paid is 0.8.

a)Find the price to be paid for this issue for an investor to earn yield i(2)=.18 on the expected payments.

b) based on the price found in part (a), find the yield to maturity if all payments are actually made.

c)Suppose that the risk of default on the redemption amount is only 10%, but the other default risks are as stated. Repeat part a) and b)