The formula for calculating the risk premium on bonds is given by 1 + i = (1 p)(1 + i + x) + p(z) where p is the probability that the bond issuer goes bankrupt, i is the nominal policy interest rate, and x is the risk premium. In the event of bankruptcy, the bond holder receives an amount z > 0. (a) Find the expression for calculating the probability of bankruptcy?

(b) Using the formula you derived in part (a) above, calculate the probability of bankruptcy when the risk premium is 0.024 (or 2.4%), the nominal policy rate is 0.046 (or 4.6%), and the amount received in the event of bankruptcy is 0.67.