Miller has retired recently from his job and is currently 70 years of age. He wants to plan for retirement income for himself. He is contemplating entering into an annuity contract with Alight Insurance Company. This contract will provide him an equal sum of money each year for the rest of his life. To receive this continued yearly benefit, he should invest a lump sum amount at the beginning of the contract i.e. now. Insurance Company, based on his health records and their own models, estimates Miller's life expectancy to be 15 years. Hence, the insurance company will do the calculations based on this estimate irrespective of the actual number of years for which Miller lives.

(i.) What initial investment should be made by Miller (at the beginning of the contract), such that the amount that he receives at the end of every year is equal to Rs.100000 per year? Assume that the interest rate used by Alight Insurance Co. is 5%.

(ii.) What initial investment should be made by Miller (at the beginning of the contract), such that the amount that he receives at the end of every year is equal to Rs.100000 per year? Assume that the interest rate used by Alight Insurance Co. is 10%.

(iii.) Suppose that Miller has made an initial investment of Rs.300000, what is the yearly amount that he would receive? Assume that the interest rate used by Alight Insurance Co. is 5%.

(iv.) Suppose that Miller has made an initial investment of Rs.300000, what is the yearly amount that he would receive? Assume that interest rate used by Alight Insurance Co. is 10%.

(v.) Compare the answers in part (iii.) and (iv.) and comment on the difference.