IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events
A policy has sum assured Rs 30,000 payable immediately on death and premiums of Rs 1,200 per year paid continuously. At a certain time the policy value is Rs 5,000 and the force of interest is 0.06. For the policy value to be momentarily stationary (dV/dt = 0) at that time, what must the force of mortality be?
The force of mortality must be 0.06. Interest on the policy value (300) plus premium (1,200) totals 1,500, which must equal μ times the sum at risk of 25,000, giving μ = 0.06.
- A0.0600Correct
- B0.0500
- C0.0480
- D0.0120
- 0.0720
Explanation
Setting dV/dt = 0: 0.06×5,000 + 1,200 = μ(30,000 − 5,000), so 1,500 = 25,000μ and μ = 0.06. Using S instead of S − V gives 0.05. Using only the premium gives 0.048.
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