Question

2. A three year temporary life annuity issued to (x) pays $10,000 at the beginning of each year, while (x) survives. Assume qe = .05 is constant, and compound interest i=8%. Compute the actuarial present value of the annuity.

Answer 1

Let the current time be denoted by 0. The annuity holder will get annuity payments at times 0, 1, 2 provided he is alive at the time of annuity payment. ? Amount received at (t=0) time 0.1 The holder will be alive today. So, the amount paid at dr0 is 10000 Amount received at (t-1) time I The probability of a person dying in any given year is 9x=0.05. Thus, the probability of survival in a given year is Pa = 1-9x = 0.95 Thus amount received at time I is 10000 X0.95 - 9500 similarly, the person receives the thind payment if he survives first two years

le 10000 X 0.95X0.95 - 79025 This can be shown on number line as follows: 10000 9500 9025 23. Now Discounting these at i = 8% to compute value, say PV cash flows the present PV = 10000 + 20. 9500 4 9025 (170.08). (1+0.08) PV - $26533.78