An insurance company issued, to a life aged 50, an annuity-immediate contract which pays $ 100 at the End of Each Month as long as the annuitant is alive. But, no payments are made after 20 years. Use the Standard Ultimate Survival Mortality and 5% annual interest rate. Assume mortality follows UDD in between integer ages. a) Write the Random Variable, Y*, using standard actuarial notation, which represents the Present Value of the above benefit. b) Write the expression for E [Y*] (without the use of a Random Variable) using standard actuarial notation. c) Write the expression for E [Y*) using only probabilities of survival. d) Write the Expression for E [Y*] where the summation is over possible years of death. e) Calculate the value E (Y") (5 decimals) An insurance company issued, to a life aged 50, an annuity-immediate contract which pays $ 100 at the End of Each Month as long as the annuitant is alive. But, no payments are made after 20 years. Use the Standard Ultimate Survival Mortality and 5% annual interest rate. Assume mortality follows UDD in between integer ages. a) Write the Random Variable, Y*, using standard actuarial notation, which represents the Present Value of the above benefit. b) Write the expression for E [Y*] (without the use of a Random Variable) using standard actuarial notation. c) Write the expression for E [Y*) using only probabilities of survival. d) Write the Expression for E [Y*] where the summation is over possible years of death. e) Calculate the value E (Y") (5 decimals)