actuarial present value of one unit of an n-year term insurance policy payable at the moment of death can be found similarly by integrating from 0 to n. The actuarial present value of an n year pure endowment insurance benefit of 1 payable after n years if alive, can be found as In practice the information available about the random variable G (and in turn T) may be drawn from life tables, which give figures by year. For example, a three year term life insurance of $100,000 payable at the end of year of death has actuarial present value For example, suppose that there is a 90% chance of an individual surviving any given year (i.e. T has a geometric distribution with parameter p = 0.9 and the set {1, 2, 3, ...} for its support). Then and at interest rate 6% the actuarial present value of one unit of the three year term insurance is so the actuarial present value of the $100,000 insurance is $24,244.85. In practice the benefit may be payable at the end of a shorter period than a year, which requires an adjustment of the formula. Life annuity The actuarial present value of a life annuity of 1 per year paid continuously can be found in two ways: Aggregate payment technique (taking the expected value of the total present value): This is similar to the method for a life insurance policy. This time the random variable Y is the total present value random variable of an annuity of 1 per year, issued to a life aged x, paid continuously as long as the person is alive, and is given by: where T=T(x) is the future lifetime random variable for a person age x. The expected value of Y is: Current payment technique (taking the total present value of the function of time representing the expected values of payments): where F(t) is the cumulative distribution function of the random variable T. The equivalence follows also from integration by parts. In practice life annuities are not paid continuously. If the payments are made at the end of each period the actuarial present value is given by Keeping the total payment per year equal to 1, the longer the period, the smaller the present value is due to two effects: The payments are made on average half a period later than in the continuous case. There is no