1. a) Derive the Macaulay duration for: a term annuity; a par bond; and, a life annuity assuming arithmetically declining survival rates.b) Using your solution from part a) and an interest rate of 3.25%, solve for the Macaulay duration of a life annuity for a 42-year-old person that cannot live beyond 95 years. Be sure to provide the numerical solutions to the numerator and denominator. Verify your answer using a discrete derivative.