Assume a corporate bond with a $$1000$ face value matures $5$ years and $7$ months from today and has an

annual coupon rate of $8\%$ paid semiannually. There is a $10\%$ chance that the issuer will default at

maturity. If the firm defaults, it will pay $80\%$ of what is promised $($final coupon $+$ face value$)$ at maturity.

Treasuries with the same maturity earn a yield to maturity of $2\%$ and investors in these corporate bonds

demand a $3\%$ risk premium over the current rate on Treasuries $($thus requiring an expected return of

$5\%)$ to compensate for the risk they face $($All rates are APRs with semiannual compounding$).$

Calculate the clean price of the bond.