IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
Which statement about annuities payable continuously on joint-life and last-survivor statuses is correct, assuming independent lives and the same force of interest?
The last-survivor annuity is at least as large as each single-life annuity, because payments continue whenever either life survives, giving a payment probability at least that of either life alone. The joint-life annuity is the smallest of the three.
- AThe last-survivor annuity is never greater than the joint-life annuity.
- BThe joint-life annuity equals the sum of the single-life annuities.
- CThe last-survivor annuity is at least as large as each single-life annuity.Correct
- DThe joint-life annuity is at least as large as each single-life annuity.
- The last-survivor annuity equals the joint-life annuity when both lives are the same age.
Explanation
The last-survivor status continues whenever either life survives, so its payment probability is at least that of either single life; hence its annuity is at least each single-life annuity. The joint-life status is the shortest, so it is no larger than the single-life annuities.
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