Question

An insurance company offers two accident policies. Policy A has a premium of $2,000 with a deductible of $800. Policy B has a premium of $2,400 with a deductible of $200. The probability of an accident costing more than $800 in a given year is 15%. Assume a person has at most one accident a year and no accidents costing less than $800. Complete each statement.

a. The annual expected cost to the owner for Policy A is $ ____________
b. The annual expected cost to the owner for Policy B is $ ____________
c. Policy _____________ has the lesser annual expected total cost to owner.

Answer 1

a. The annual expected cost to the owner for Policy A is $ _____2,120____

b. The annual expected cost to the owner for Policy B is $ ____2,430_____

c. Policy ____A____ has the lesser annual expected total cost to owner.

Step-by-step explanation:

a) Data and Calculations:

Policy A Policy B

Annual Premium $2,000 $2,400

Deductible $800 $200

Probability of an accident

costing >$800 = 15% 15%

Probability of no accident 85% 85% (100% - 85%)

Annual expected cost = $2,120 $2,430

Policy A = $2,120 ($2,000 + ($800 * 15%))

Policy B = $2,430 ($2,400 + ($200 * 15%))