IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
At a rate of interest of 5% p.a., the annuity values are a_x = 12.00, a_y = 14.00 and a_xy = 10.50, all payable annually in arrears while the status survives. Assuming independent lives, what is the value of an annuity of ₹1 p.a. payable in arrears while at least one of (x) and (y) is alive?
The value is 15.50. The last survivor annuity equals the sum of the two single-life annuities minus the joint-life annuity, so 12.00 + 14.00 − 10.50 = 15.50. Each payment is made while at least one life survives.
- A15.50Correct
- B16.50
- C26.00
- D24.50
- 14.00
Explanation
For the last survivor status, a_x̄ȳ = a_x + a_y − a_xy = 12.00 + 14.00 − 10.50 = 15.50. Option 16.50 comes from wrongly adding 1 to the result, and 26.00 is just a_x + a_y with the joint-life term omitted.
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