An annuity is a financial instrument that pays out a constant amount of income per period for as long as the annuitant (i.e. annuity purchaser) is alive. Let P be the expected present value of annuity payments. Let a denote annuity income payment per period, m denote the probability of dying by next period (a.k.a mortality rate) and r denote the interest rate Use the recursive asset pricing formula P = a + EP'/1+r to show that P = a/r + m. b) Suppose that an elderly annuitant has 500,000 in wealth and uses this wealth to purchase an annuity. Calculate the annual payment that the annuitant should expect if r = 0.05 and m = 0.03 per year. Explain how your answer is related to equilibrium economic profit of a financial institution that issued the annuity. (ii) Life insurance premium A life insurance policy is a financial contract that collects a premium of p per period from the insured and pays out a lump sum benefit B upon the death of the insured. Let m denote the mortality rate, r denote the interest rate and V denote the expected present value of economic profits of the insurance company on this policy. Use the recursive asset pricing formula V = p + EV'/1 + r to express equilibrium life insurance premium, p, through exogenous variables. Explain your answer and