SOA FAM-Fundamentals Of Actuarial Mathematics
Exam | Practice Questions And Answers 2026/2027 |
Complete Questions And Answers (Verified Answers) |
Exam Prep | Comprehensive Exam Guide 2026&2027
1. An automobile insurer changes a policy by increasing the deductible from $500 to $1,000
while leaving all other terms unchanged. For a fixed loss amount, what is the primary
effect of the higher deductible on the insurer's payment?
A. The insurer's payment increases by $500
B. The insurer's payment decreases by up to $500
C. The insurer's payment is unchanged for every loss
D. The insurer pays the entire loss once the deductible is exceeded
Answer: B
The higher deductible shifts a larger portion of each covered loss to the insured. For losses
exceeding both deductibles, the insurer's payment decreases by $500.
2. A claim has an ultimate loss of $8,000 and is subject to a $2,000 ordinary deductible.
What amount is payable by the insurer?
A. $6,000
B. $8,000
C. $2,000
D. $10,000
Answer: A
With an ordinary deductible, the insurer pays the loss amount minus the deductible when the
loss exceeds the deductible: $8,000 − $2,000 = $6,000.
3. An insurer purchases per-occurrence excess-of-loss reinsurance with a $100,000
retention and a $400,000 limit. A covered claim is $350,000. How much is paid by the
reinsurer?
A. $100,000
B. $250,000
C. $350,000
D. $400,000
Answer: B
The reinsurer covers the portion above the $100,000 retention, subject to the $400,000 limit.
Thus, $350,000 − $100,000 = $250,000.
,4. A proportional quota-share treaty provides that the reinsurer receives 30% of premiums
and pays 30% of covered losses. If a covered claim is $90,000, what amount is allocated to
the reinsurer?
A. $21,000
B. $27,000
C. $30,000
D. $63,000
Answer: B
Under a 30% quota-share arrangement, the reinsurer pays 30% of the covered claim, or 0.30 ×
$90,000 = $27,000.
5. A loss of $50,000 is subject to an ordinary deductible of $5,000 and then a policy limit of
$40,000. What is the insurer's payment?
A. $35,000
B. $40,000
C. $45,000
D. $50,000
Answer: A
After the $5,000 deductible, the covered amount is $45,000. The $40,000 policy limit then
caps the insurer's payment at $40,000.
6. A portfolio's losses are subject to inflation of 5%. A historical loss of $20,000 is adjusted
to the current level using this inflation factor. What is the adjusted loss?
A. $20,500
B. $21,000
C. $21,500
D. $22,000
Answer: B
Applying 5% inflation gives $20,000(1.05) = $21,000.
7. A claim has a loss amount of $120,000. The policy has a $20,000 deductible and a $75,000
limit above the deductible. What is the insurer's payment?
A. $20,000
B. $75,000
C. $95,000
D. $100,000
Answer: B
The loss after the deductible is $100,000, but the policy limit allows only $75,000 to be paid.
,8. An insurer has an excess-of-loss treaty with a retention of $250,000 and a limit of
$500,000. A covered claim is $900,000. What amount is paid by the reinsurer?
A. $250,000
B. $400,000
C. $500,000
D. $650,000
Answer: C
The loss above retention is $900,000 − $250,000 = $650,000, but the reinsurance limit is
$500,000.
9. Which coverage modification most directly reduces the insurer's payment on small
claims while leaving larger claims relatively less affected?
A. Increasing the deductible
B. Increasing the policy limit
C. Removing the deductible
D. Increasing the coinsurance percentage paid by the insurer
Answer: A
A higher deductible shifts the initial portion of each loss to the insured and therefore has its
greatest proportional effect on smaller losses.
10. A loss distribution is subject to an ordinary deductible of $10,000. A loss of $7,000
occurs. How much does the insurer pay?
A. $3,000
B. $7,000
C. $10,000
D. $0
Answer: D
Because the loss does not exceed the ordinary deductible, there is no insurer payment.
11. A severity random variable X has mean 10 and variance 25. If Y = 2X + 5, what are the
mean and variance of Y?
A. Mean 25, variance 50
B. Mean 25, variance 100
C. Mean 15, variance 50
D. Mean 15, variance 100
Answer: B
E[Y] = 2E[X] + 5 = 25, while Var(Y) = 2²Var(X) = 100.
, 12. A continuous loss variable has cumulative distribution function F(x). The 90th
percentile is the value x such that:
A. F(x) = 0.10
B. F(x) = 0.50
C. F(x) = 0.90
D. F(x) = 1.90
Answer: C
By definition, the 90th percentile is the loss level whose cumulative probability is 0.90.
13. A severity model is scaled by multiplying every loss by 1.2. If the original mean loss is
$5,000, what is the new mean?
A. $4,167
B. $5,000
C. $5,200
D. $6,000
Answer: D
Multiplying every loss by 1.2 multiplies the mean by 1.2, giving $6,000.
14. For a Poisson frequency distribution with parameter λ, which quantity equals both the
mean and variance?
A. λ
B. λ²
C. 1/λ
D. e^λ
Answer: A
For a Poisson random variable, both the expected value and variance equal λ.
15. An insurer expects claim counts to follow a Poisson distribution with mean 3. What is
the probability of exactly zero claims?
A. e³
B. 3e⁻³
C. e⁻³
D. 1 − e⁻³
Answer: C
For a Poisson variable, P(N = 0) = e⁻λ = e⁻³.
16. Which frequency distribution has the defining property that its variance exceeds its
mean when the parameterization has positive overdispersion?
Exam | Practice Questions And Answers 2026/2027 |
Complete Questions And Answers (Verified Answers) |
Exam Prep | Comprehensive Exam Guide 2026&2027
1. An automobile insurer changes a policy by increasing the deductible from $500 to $1,000
while leaving all other terms unchanged. For a fixed loss amount, what is the primary
effect of the higher deductible on the insurer's payment?
A. The insurer's payment increases by $500
B. The insurer's payment decreases by up to $500
C. The insurer's payment is unchanged for every loss
D. The insurer pays the entire loss once the deductible is exceeded
Answer: B
The higher deductible shifts a larger portion of each covered loss to the insured. For losses
exceeding both deductibles, the insurer's payment decreases by $500.
2. A claim has an ultimate loss of $8,000 and is subject to a $2,000 ordinary deductible.
What amount is payable by the insurer?
A. $6,000
B. $8,000
C. $2,000
D. $10,000
Answer: A
With an ordinary deductible, the insurer pays the loss amount minus the deductible when the
loss exceeds the deductible: $8,000 − $2,000 = $6,000.
3. An insurer purchases per-occurrence excess-of-loss reinsurance with a $100,000
retention and a $400,000 limit. A covered claim is $350,000. How much is paid by the
reinsurer?
A. $100,000
B. $250,000
C. $350,000
D. $400,000
Answer: B
The reinsurer covers the portion above the $100,000 retention, subject to the $400,000 limit.
Thus, $350,000 − $100,000 = $250,000.
,4. A proportional quota-share treaty provides that the reinsurer receives 30% of premiums
and pays 30% of covered losses. If a covered claim is $90,000, what amount is allocated to
the reinsurer?
A. $21,000
B. $27,000
C. $30,000
D. $63,000
Answer: B
Under a 30% quota-share arrangement, the reinsurer pays 30% of the covered claim, or 0.30 ×
$90,000 = $27,000.
5. A loss of $50,000 is subject to an ordinary deductible of $5,000 and then a policy limit of
$40,000. What is the insurer's payment?
A. $35,000
B. $40,000
C. $45,000
D. $50,000
Answer: A
After the $5,000 deductible, the covered amount is $45,000. The $40,000 policy limit then
caps the insurer's payment at $40,000.
6. A portfolio's losses are subject to inflation of 5%. A historical loss of $20,000 is adjusted
to the current level using this inflation factor. What is the adjusted loss?
A. $20,500
B. $21,000
C. $21,500
D. $22,000
Answer: B
Applying 5% inflation gives $20,000(1.05) = $21,000.
7. A claim has a loss amount of $120,000. The policy has a $20,000 deductible and a $75,000
limit above the deductible. What is the insurer's payment?
A. $20,000
B. $75,000
C. $95,000
D. $100,000
Answer: B
The loss after the deductible is $100,000, but the policy limit allows only $75,000 to be paid.
,8. An insurer has an excess-of-loss treaty with a retention of $250,000 and a limit of
$500,000. A covered claim is $900,000. What amount is paid by the reinsurer?
A. $250,000
B. $400,000
C. $500,000
D. $650,000
Answer: C
The loss above retention is $900,000 − $250,000 = $650,000, but the reinsurance limit is
$500,000.
9. Which coverage modification most directly reduces the insurer's payment on small
claims while leaving larger claims relatively less affected?
A. Increasing the deductible
B. Increasing the policy limit
C. Removing the deductible
D. Increasing the coinsurance percentage paid by the insurer
Answer: A
A higher deductible shifts the initial portion of each loss to the insured and therefore has its
greatest proportional effect on smaller losses.
10. A loss distribution is subject to an ordinary deductible of $10,000. A loss of $7,000
occurs. How much does the insurer pay?
A. $3,000
B. $7,000
C. $10,000
D. $0
Answer: D
Because the loss does not exceed the ordinary deductible, there is no insurer payment.
11. A severity random variable X has mean 10 and variance 25. If Y = 2X + 5, what are the
mean and variance of Y?
A. Mean 25, variance 50
B. Mean 25, variance 100
C. Mean 15, variance 50
D. Mean 15, variance 100
Answer: B
E[Y] = 2E[X] + 5 = 25, while Var(Y) = 2²Var(X) = 100.
, 12. A continuous loss variable has cumulative distribution function F(x). The 90th
percentile is the value x such that:
A. F(x) = 0.10
B. F(x) = 0.50
C. F(x) = 0.90
D. F(x) = 1.90
Answer: C
By definition, the 90th percentile is the loss level whose cumulative probability is 0.90.
13. A severity model is scaled by multiplying every loss by 1.2. If the original mean loss is
$5,000, what is the new mean?
A. $4,167
B. $5,000
C. $5,200
D. $6,000
Answer: D
Multiplying every loss by 1.2 multiplies the mean by 1.2, giving $6,000.
14. For a Poisson frequency distribution with parameter λ, which quantity equals both the
mean and variance?
A. λ
B. λ²
C. 1/λ
D. e^λ
Answer: A
For a Poisson random variable, both the expected value and variance equal λ.
15. An insurer expects claim counts to follow a Poisson distribution with mean 3. What is
the probability of exactly zero claims?
A. e³
B. 3e⁻³
C. e⁻³
D. 1 − e⁻³
Answer: C
For a Poisson variable, P(N = 0) = e⁻λ = e⁻³.
16. Which frequency distribution has the defining property that its variance exceeds its
mean when the parameterization has positive overdispersion?
