Worked solution · Exam P
This Exam P sample reference tests Insurance Payment Variables. This is an expected payment calculation under a 500 deductible followed by a fixed premium loading. Applying the deductible to each positive loss gives expected payment 945; adding 75 gives premium 1,020 and choice C.
Independent solution
Setup
Express the insurer payment as the loss above the deductible, floored at zero.
Model
Map each loss amount to its corresponding payment.
Compute
Weight the payments by their probabilities, then add the stated amount to determine the premium.
Answer
The required premium is 1,020.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A device repair loss L is 0, 400, or 1,000 with probabilities 0.50, 0.30, and 0.20. A plan reimburses 50% of the amount above a 200 deductible, subject to a maximum reimbursement of 300. The plan premium equals the expected reimbursement plus a fixed charge of 20. Calculate the premium.
The three reimbursements are 0, 100, and 300 after applying the deductible, 50% share, and cap. Their expected value is 90, and the fixed charge raises the premium to 110, choice D.
Setup
Write the reimbursement transformation including the deductible, sharing percentage, and cap.
Model
Evaluate the reimbursement at each possible loss.
Compute
Take the expected reimbursement and then add the fixed charge.
Answer
The plan premium is 110.
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