Answer:
The minimum amount that he can expect to pay for his premium is $1600
Step-by-step explanation:
Let the minimum amount he can expect to pay for his premium be $P. The minimum premium occurs when the insurance company expected profit is zero.
If the man lives for one years the gain would be $P and the probability of the man living for one year = 0.92.
If the man dies during one year the gain is $(P - 20000) and the probability of him dying within one year is (1 - 0.92 = 0.08)
Therefore insurance company expected profit is:
0.92P + 0.08(P - 20000)
Since The minimum premium occurs when the insurance company expected profit is zero,
0.92P + 0.08(P - 20000) ≥ 0
0.92P + 0.08P - 1600 ≥ 0
P - 1600 ≥ 0
P ≥ 1600
Therefore the minimum amount that he can expect to pay for his premium is $1600
