Assuming a maximum age of 108 (N = 43) and 4% interest, a life insurer calculating with mortality statistics requires €105,513 capital to pay for a €10,000 annuity for life, for a 65-year old male. For a 65-year old female, this would be €126,698.

The difference is explained by the expected longer longevity of females:1) How much should a 25-year old female pay to receive €10,000 p.a. starting at 65, for as long as she lives (without mortality)? Hint: calculate an Annuity Due.2) The life insurer is using mortality statistics and knows that out of 10,000,000 new-born, 9,936,640 are alive at 25, 9,662,170 at 50 and 8,861,300 at 65-years.
3) How much should a 25-year old female pay to receive €10,000 p.a. starting at 65, as long as she is alive (with mortality)?