Calculating the risk premium on bonds

The text presents a formula where

(1 + i) = (1 - p)(1 + i + x) + p(0)

p is the probability the bond does not pay at all (the bond issuer is bankrupt) and has a zero return.

i is the nominal policy interest rate.

x is the risk premium

a. If the probability of bankruptcy is zero, what is the rate of interest on the risky bond?

b. Calculate the probability of bankrupcty when the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%.

c. Calculate the nominal interest rate for a borrower when the probability of bankruptcy is 1% and the nominal policy rate of interest is 4%.

d. Calculate the nominal interest rate for a borrower when the probability of bankruptcy is 5% and the nominal policy rate of interest is 4%.

e. The formula assumes that payment upon default is zero. In fact, it is often positive. How would you change the formula in this case?