6. A one-year US Treasury strip is currently yielding 1.78 percent (i=178 basis points) and an A-rated discount bond with similar maturity is yielding 2.35 percent (k=235 basis points). If the expected recovery from collateral () in the event of default is 50 percent of principal and interest, what is the probability of repayment (p) of the A rated bond (not defaulting)? What is the probability of default (1-p)?

Hint:

p(1 + k) + g (1 - p)(1 + k) = 1 + i. Solve for the probability of repayment (p):