Alife insurer is about to issue a 30-year deferred annuity-due with annual payments of $20 000 to a select life aged 35. The policy has a single premium which is refunded without interest at the end of the year of death if death occurs during the deferred period. (a) Calculate the single premium for this annuity. (b) The insurer offers an option that if the policyholder dies before the total annuity payments exceed the single premium, then the balance will be paid as a death benefit, at the end of the year of death. Calculate the revised premium. This is called a Cash Refund Payout Option.