A government issuing a 5-year 15% bond wit face amount 1,000,000,000. Th perception in the investment community is that the government is somewhat unstable, and it is forecast that there is a 10% chance the government will default on interest payments by the first or second years, a 20% chance of default by the third or fourth years, and a 25% chance of default (on interest and principal) by the fifth year. All probabilities are unconditional ( measured from time 0, so that, for instance, the probability that the 7th coupon is paid is .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 par (a), find the yield to maturity if all payments are actually made.