A single bank is considering two options: First, it can make a $$200,000$ mortgage loan for a customer with a $10$ percent probability of default, or second, it can buy a $$200,000$ security representing a bundle of $100$ mortgage loans, which break down as shown in the table below.

You can calculate the weighted risk for each firm category by multiplying the percentage of loans represented $($for example, the first tier includes $35$ loans, which is $35/100=35\%$ of the total$)$ times the probability of default on loans of that category.

Instructions: Round your answers to three decimal places.

a$.$ Calculate the weighted risk for each type of loan, then add together the weighted risks to come up with an overall expected default risk for this financial investment.

Number of Loans

Probability of Default $(\%)$

Weighted Risk

$353\%$

$2512\%$

$201\mathrm{.}5\%$

$204\mathrm{.}5\%$

Adding together the weighted risks, the expected default risk for the security is: $\%.$

b$.$ If the bank is willing to take on only projects for which the default risk is $6\%$ or less, it should choose the $.$