Consider a hypothetical insurance company that has been selling GICs for many years. A year from today, you expect the aggregate payment for the maturing GICs to be 2!) million. Thereafter, you project payments for maturing GICs to grow forever at an annual rate of 1%. The term structure is at at 9%, and the current assets of the company consist of 3111} million in cash. Rates are with annual compounding. {a} What is the present value of the companyls GIC liabilities? 1What is the company's net worth?I (b) Suppose the company keeps its assets in cash. Explain why this is a dangerous choice. To provide an example, consider a parallel shift in the term structure to 5% {the term structure remains at}. (c) Quantify the company's interest-rate risk by calculating Macaulay duration and modied duration of the GIC liabilities. Show that the Macaulay duration is 13.625 years. H111! 1': Use the formula for the present value of a growing perpetuity, and the fact that modied duration is related to the derivative of the present value. Hint 2: Alternatively, you can assume that payments do not continue forever, but end at some very distant future date. Take this date to by 21} years, 51] years, 1111} years, . .. Use Excel to show that the ensuing duration approaches 131525 years