A woman about to retire is concerned about her future financial security so she buys an annuity that pays $1,000 a month for twenty years starting in a year’s time. One insurance company will sell her an annuity at a discount rate of .96 per year and another at a discount rate of .95 per year. (i) what is the monthly discount rate associated with each of these products? (ii) write down the sum that gives the present value of these annuity payments at a disount rate of d per month. (iii) find a formula for this sum. This is the cost of the annuity. (iv) Hence evaluate the cost of the annuities from each of the insurance companies. (v) How much more will she receive in payments than she pays for initially for each of the two policies?