1. A person aged 65 exact has finished paid employment and is looking to retire and use their savings to provide an income until they die. They have savings of 100,000 to be used to do this. You are asked to calculate a range of benefits that can be bought using the whole of the lump sum, assuming an interest rate of 4% p.a. and mortality AM92(ult). (a) Calculate the amount of income I that the person can receive if they use the lump sum to buy an annuity for life payable annually in advance. [2 marks] (b) The person wants to have extra income of 500 to pay for a nice holiday (where the suns shines a bit more than it does in Manchester), once every two years. They decide that they would like the additional 500 to pay for these holidays and that the first additional 500 should be paid at age 66 exact. Therefore they want an annual income stream of amount I*, I* + 500, I* I* + 500, ....... Calculate the amount I* if the lump sum is used to buy this benefit. [6 marks] 1. A person aged 65 exact has finished paid employment and is looking to retire and use their savings to provide an income until they die. They have savings of 100,000 to be used to do this. You are asked to calculate a range of benefits that can be bought using the whole of the lump sum, assuming an interest rate of 4% p.a. and mortality AM92(ult). (a) Calculate the amount of income I that the person can receive if they use the lump sum to buy an annuity for life payable annually in advance. [2 marks] (b) The person wants to have extra income of 500 to pay for a nice holiday (where the suns shines a bit more than it does in Manchester), once every two years. They decide that they would like the additional 500 to pay for these holidays and that the first additional 500 should be paid at age 66 exact. Therefore they want an annual income stream of amount I*, I* + 500, I* I* + 500, ....... Calculate the amount I* if the lump sum is used to buy this benefit. [6 marks]