3. In this question we will design a loan guarantee - also known as a credit-default swap when applied to bonds and as deposit insurance when applied to bank deposits - for the loan in the unit trust from the first lecture. Loan guarantees, as the name suggests, guarantee the performance of the loan and, as such, hedge default risk. Use a detailed payoff diagram of the (i) loan without the loan guarantee, (ii) loan guarantee, and (iii) loan with a loan guarantee for the following situations: (a) Your parents want their loan to be risk-free. Hint: review the construction of a synthetic risk-free loan. (b) Your parents want to have at least USD 50 in the event of default. For each diagram provide a brief explanation of how the loan guarantee works