Life Insurance: Your company sells life insurance. You charge a 55 year old man

Question

Life Insurance: Your company sells life insurance. You charge a 55 year old man $60 for a one year, $100,000 policy. If he dies over the course of the next year you pay out $100,000. If he lives, you keep the $60. Based on historical data (relative frequency approximation) the average 55 year old man has a 0.9995 probability of living another year (a) What is your expected profit on this policy? (b) What is an accurate interpretation of this value? o It represents the average profit per policy sold that you would expect if you sold a lot of these policies It represents the loss on every policy sold. It is meaningless because the insurance company never makes this amount on a policy O It represents the profit on every policy sold.

Explanation / Answer

(a) PROBABILITY OF LIVING MAN FOR ANOTHER YEAR = 0.9995 ( LET P1 ) AND PREMIUM CHARGED $60 ( LET X1) , PROBABILITY OF HIS SURVIVAL = (1 - 0.9995 ) = 0.0005 ( LET P2 ) , AND IF THE PERSON DIES WE HAVE TO PAY $ 1,00,000 (let P2 )

NOW EXPECTED PROFIT = P1,X1 + P2.X2    = 0.9995 X 60 + 0.0005X( - 1,00,000 ) [ X2 WILL BE NEGATIVE AS IT IS LOSS FOR ME ]

HENCE EXPECTED PROFIT = 59.97 - 50 = $ 9.97

(b) ACCURATE INTERPRETATION OF THIS VALUE IS ` IT REPRESENT THE PROFIT ON EVERYPOLICY SOLD `

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