6. Sam, aged 35, has just taken out a home mortgage loan where he will pay $1,000 at the beginning of each month for 30 years. He was also required to purchase an insurance policy that will pay any remaining (unpaid) payments should he die within the 30-year period. Assume the mortality follows the SOA-LTAM Standard Ultimate Life Table with interest rate i = 5%. (a) (5 points) Write out the present value random variable of this policy, denoted by Z. (b) (9 points) Calculate the Expected Present Value (EPV) of this policy, i.e., E(Z). Use the Woolhouse's three terms formula and the constant force of mortality for fractional ages. 6. Sam, aged 35, has just taken out a home mortgage loan where he will pay $1,000 at the beginning of each month for 30 years. He was also required to purchase an insurance policy that will pay any remaining (unpaid) payments should he die within the 30-year period. Assume the mortality follows the SOA-LTAM Standard Ultimate Life Table with interest rate i = 5%. (a) (5 points) Write out the present value random variable of this policy, denoted by Z. (b) (9 points) Calculate the Expected Present Value (EPV) of this policy, i.e., E(Z). Use the Woolhouse's three terms formula and the constant force of mortality for fractional ages