$(4$pts each$)$ Suppose that the risk$-$free zero curve is flat at $6\%$ per annum with continuous compounding and that defaults can occur half way through each year in a new two$-$year credit default swap. Suppose that the recovery rate is $20\%$ and the default probabilities each year conditional on no earlier default are $3\%,$ Estimate the credit default swap spread. Assume payments are made annually.

$(1)$ Find the table corresponding to unconditional default probabilities and survival probabilities.

$(2)$ Calculate the present value of the $s$ per year.

$(3)$ Calculate the present value of the expected payoffs when the notional principal is $$1.$

$(4)$ Calculate the present value of accrual payments.

$(5)$ Evaluate the credit default swap spread $s.$