A four$-$year corporate bond provides a coupon of $4\%$ per year payable semiannually and has a

yield of $5\%$ expressed with continuous compounding. The risk$-$free yield curve is flat at $3\%$ with

continuous compounding. Assume that defaults can take place at the end of each year

$($immediately before a coupon or principal payment and the recovery rate is $30\%.$ Estimate the

risk$-$neutral default probability on the assumption that it is the same each year.