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Answer: USD 6,389
## Explanation The expected payout is calculated as: **Payoff = Insurance Amount × Probability of Death at Age 72** Where the probability of death at age 72 is: - **Probability that the policyholder survives to age 72** × **Probability of death within 1 year at age 72** The calculation: - Insurance Amount = USD 350,000 - Probability of surviving to age 72 = Cumulative survival probability at 72 = 0.79911 - Probability of death within 1 year at age 72 = 0.018861 **Expected Payout = 350,000 × 0.79911 × 0.018861 = 6,389** **Why other options are incorrect:** - **A**: Uses incorrect probability calculation - **B**: Uses cumulative survival probability at 71 instead of 72 - **D**: Uses incorrect ratio of survival probabilities This calculation represents the expected value of the insurance payout, considering the probability that the policyholder survives to age 72 and then dies during that year.
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An actuary at an insurance company is validating a newly implemented model that calculates the expected future payoff of term life policies. The actuary spot checks the calculations by using an example of a 70-year-old policyholder with a term life insurance policy. The policy pays out USD 350,000 if the policyholder dies between the ages of 72 and 73, and pays nothing otherwise. The actuary uses the following information to calculate the expected future payoff of this policy:
| Age (years) | Probability of death within 1 year | Cumulative survival probability |
|---|---|---|
| 70 | 0.015413 | 0.82573 |
| 71 | 0.017089 | 0.81301 |
| 72 | 0.018861 | 0.79911 |
| 73 | 0.020705 | 0.78404 |
Assuming any payout occurs at the end of the year, what is the closest value to the expected payout on this policy?
A
USD 5,358
B
USD 5,367
C
USD 6,389
D
USD 6,477
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