可以解釋吗

问题如下：

An actuary at an insurance company is validating a newly implemented model that calculates the expected future payoff of term life insurance policies. The actuary spot checks the model’s 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 at the age of 72 before turning 73, and pays nothing otherwise. The actuary uses the following information to calculate the expected future payoff of this policy:

Assuming any payout occurs at the end of the year, what is the closest value to the expected payout on this policy?

选项：

A.

USD 5,358

B.

USD 5,367

C.

USD 6,389

D.

USD 6,477

解释：

C is correct.

Payoff = amount of insurance payment * probability that the person will live until 72 and die at the age of 72 = 350,000 * (cumulative survival probability at 72/ cumulative survival probability at 70 * probability of death within 1 year at 72) = 350,000 * 0.79911/0.82573 * 0.018861 = 6,389

A is incorrect. Probability of dying at 72 is calculated as: cumulative survival probability at 70 * (1 − probability of death within 1 year at 71) * probability of death within 1 year at 72

B is incorrect. Probability of dying at 72 is calculated as: cumulative survival probability at 71 * probability of death within 1 year at 72

D is incorrect. Probability of dying at 72 is calculated as: cumulative survival probability at 73 / cumulative survival probability at 72 * probability of death within 1 year at 72