You are the owner of a finance company that extends one$-$year loans for people to buy appliances and other household goods. A young MBA that you just hired suggests that since the default risk of your loans is all diversifiable $($i$.$e$.,$ the correlation of the return on the loans with the market is zero$),$ you should charge your customers the risk$-$free rate. $($a$)$ Assuming the default risk is completely diversifiable, does the CAPM tell you to set the interest rate on your loans equal to the risk$-$free rate? $($b$)$ Assume the risk$-$free rate is $10\%$ and that the probability of default is $5\%$ for the next year. In addition, assume that if a borrower defaults, all the principal but no interest is paid back. What rate should your finance company charge for loans over the next year?