Question

Mosey incurs underwriting costs when a policy is written and claims settlement costs when a claim is settled. The administrative costs of processing an application is 10% of the premium charged when the policy is written. The cost of settling a claim is $175 per claim, when claim is settled. The fair profit loading is 6%. If the policy has a $5,000 deductible and claims are paid 2.5 years after the premium is collected, what is the fair premium? Assume the applicable effective annual rate is 4%.

Mosey faces the following loss distribution:

Size of Loss	Probability of Loss
40,000	0.006
30,000	0.015
15,000	0.02
7,500	0.025
2,200	0.035
0	0.899

Answer 1

		A	B=A-5000	C	D=B*C
		Size of loss	Payable after deduction	Probability	Size of loss*Probability
		$40,000	$35,000	0.006	$210
		$30,000	$25,000	0.015	$375
		$15,000	$10,000	0.02	$200
		$7,500	$2,500	0.025	$63
		$2,200	$0	0.035	$0
		$0	$0	0.899	$0
				Sum	$848
	Expected Payment in 2.5 years	$848
	Cost of settling claim	$175
	Total Cost at end of 2.5 years	$1,023
	Discount Rate =4%	0.04
	Present Value of Cost	$927	1023/(1.04^2.5)
	Assume fair premium =X
	Administrative cost in year 0=	0.1X
	Present Value of Total Cost	927+0.1X
	Profit Loading	6%
	Fair Premium =(927+0.1X)*1.06=	X
	982.62+0.106X=X
	X(1-0.106)=982.62
	X=982.62/(1-0.106)=	$1,099
	Fair Premium =	$1,099