# W6Tute 1001 - Examples x is the actuarial notation for a...

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Examples ¨ a x is the actuarial notation for a life annuity due of 1 per period to a life aged x as long as they are alive. ¨ a x : n represents a life annuity due of 1 per period to a life aged x as long as they are alive, making at most n payments. Suppose that the applicable survival function is s ( x ) = 1 - x 100 for 0 x < 100, and the force of interest is constant, with δ ( t ) 0 . 04, with t and x representing time and age in years respectively. 1. Explain why ¨ a x : n = 1 + vp x ¨ a x +1: n - 1 . 2. Determine ¨ a 50: 3 and ¨ a 51: 2 . Verify that the recursive relationship given in (1) is satisﬁed. 3. Which is larger: ¨ a 3 or ¨ a 50: 3 ? Explain why. UNSW Week 6 ACTL1001 Tutorial

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Examples Recursive Relationship ¨ a x : n represents a life annuity with at most n payments. A payment is immediately made at time zero, hence the ‘1’. In one year’s time, the annuitant is either alive, with probability p x , or is dead, with probability q x . If the annuitant is dead, they receive nothing. If they are alive,
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## This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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W6Tute 1001 - Examples x is the actuarial notation for a...

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