Exam P practice problems: Insurance: deductibles, limits and coinsurance

10 problems · Untimed · Worked solution after each answer

Payments under deductibles, policy limits, coinsurance and inflation, and the mean and variance of the loss and the payment. This drill covers topic 2 of the Exam P syllabus, Univariate Random Variables (44–50% of the exam).

2e Insurance payments with deductibles, coinsurance and limits
2f Moments of the loss and the payment

Line drawing of a claim form on a clipboard beside a small car with a dented bumper and a closed umbrella

Before you start

Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Insurance: deductibles, limits and coinsurance

Write the payment as a function of the loss X first, for example Y = 0 for X ≤ d, X − d for d < X ≤ u, and u − d above, then take its expectation.
For a nonnegative loss, E[(X − d)₊] = ∫ from d to ∞ of S(x) dx, and E[min(X, u)] = ∫ from 0 to u of S(x) dx.
Per loss averages over every loss, including those below the deductible; per payment divides by P(X > d).
Inflation scales the loss, not the deductible: with uniform inflation r, the new loss is (1 + r)X against the same d.

Create a free account before you start

Create a free account to start. Every drill includes one free attempt. An Exam P and FM pass unlocks both timed practice exams and unlimited drills for both exams.

Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).