An investor is evaluating two bonds with the same maturity but different default risks. Bond A has a yield of $5\%,$ and Bond B has a yield of $8\%.$ The investor believes that the probability of default on Bond B is $15\%$ over the holding period and estimates that, in the event of default, they will recover $30\%$ of the bond's face value $($and lose $70\%).$ The investor also has the option of investing in a risk$-$free bond with a yield of $2\%.$a$)$ Calculate the investor's expected return on Bond B$,$ considering the default risk and recovery rate.b$)$ Assuming the investor is risk$-$averse, under what conditions might the investor prefer Bond A over Bond B$,$ even though Bond B has a higher yield?Discuss the impact of risk premium and recovery rate $(30\%)$ on the investor's decision.c$)$ The investor