Question

A man wishes to purchase a life insurance policy that will pay the beneficiary $30,000 in the event that the man's death occurs during the next year. Using life insurance tables, he determines that the probability that he will live another year is 0.92. What is the minimum amount that he can expect to pay for his premium? Hint: The minimum premium occurs when the insurance company's expected profit is zero.

Answer 1

Suppose the premium amount is Y

If the person lives next year amt that insurance company gets Y ;  P(0.92)

If the person does not live next year amt that insurance company gets Y - 30000 ; P(0.08)

Expected amount = Y* 0.92 + (Y-30000) 0.08

Expected amount = 0

Y * 0.92 + (Y - 30000) 0.08 = 0

Y - 2400 = 0

Y = 2400

Scenerio	x	P(x)	x* P(x)
Does not die	2400	0.92	2208.00
Dies	-27600	0.08	-2208.00
Total	Total	1.00	0.00

ANS: Minimum premium = $2400