“150”, Aptitude Test
Questions and Answers for Actuarial Officer II -National Insurance Corporation
(NIC).
ABSTRACT
This preparation package provides 150
premium multiple-choice aptitude test questions and answers designed for
candidates preparing for the Actuarial Officer II – National Insurance
Corporation (NIC) Public Service online aptitude test in Tanzania. The
questions assess key areas of actuarial science, including probability,
statistical analysis, risk assessment, actuarial modelling, claims experience
analysis, investment performance, liabilities, forecasting, data
interpretation, and insurance risk management. Particular emphasis is placed on
practical reasoning, closely related answer choices, numerical analysis,
interpretation of actuarial information, and decision-making in an insurance
environment. The questions are structured to reflect the analytical and
challenging nature of competitive public service aptitude examinations and are
intended to strengthen candidates' understanding, accuracy, critical thinking,
and ability to apply actuarial concepts under examination conditions.
Prepared
by: Actuarial Officer II
An
author based in Dar-es-salaam.
0628729934.
Date:
August 11, 2026
Dear
applicants,
This
collection of questions and answers has been prepared to help all of you to understand
the key areas tested during the interview. The goal is to provide a useful, and
practical study guide so you can all perform confidently and fairly in the
selection process. I wish you the best of luck, and may this resource support
you in achieving success!
Warm
regards,
Actuarial
Officer II
For
Personal Use by Applicants Preparing for Actuarial Officer II -National Insurance
Corporation (NIC).
ALL
QUESTIONS ARE COMPILED TOGETHER.
1. An insurance portfolio contains 10,000
independent policies. Each policy has a 2% probability of generating a claim
during a particular year, with each claim costing exactly TZS 500,000. Assuming
the probabilities remain constant, what is the expected total claim cost for
the portfolio?
A. TZS 50 million B. TZS 100 million C.
TZS 125 million D. TZS 200 million
Answer: B
Rationale: The expected number of claims is
obtained by multiplying the number of policies by the probability of a claim:
10,000 × 0.02 = 200 expected claims. Since each claim costs TZS 500,000, the
expected total claim cost is 200 × 500,000 = TZS 100,000,000. The important
actuarial principle is that expected aggregate loss equals the expected
frequency multiplied by the expected severity when the relevant assumptions
permit this calculation.
2. An actuary observes that the
probability of a claim from a particular policyholder is 0.30. The probability
that the policyholder renews the policy is 0.80. If the probability of a claim
and renewal occurring together is 0.24, what does this imply about the
relationship between the two events?
A. They are mutually exclusive B. They
are conditionally dependent C. They are statistically independent D. They
have equal occurrence rates
Answer: C
Rationale: Two events are independent when the
probability of their joint occurrence equals the product of their individual
probabilities. Here, P(claim) × P(renewal) = 0.30 × 0.80 = 0.24, which is
exactly the stated joint probability. Therefore, the evidence is consistent
with statistical independence. Mutual exclusivity would instead require the
joint probability to be zero.
3. NIC is comparing two portfolios.
Portfolio X has an expected annual return of 10% with a standard deviation of
4%, while Portfolio Y has an expected annual return of 12% with a standard
deviation of 8%. If an analyst uses the coefficient of variation to compare
risk per unit of expected return, which portfolio has the lower relative risk?
A. Portfolio X B. Portfolio Y C. Both
portfolios D. Neither portfolio
Answer: A
Rationale: The coefficient of variation is
calculated as standard deviation divided by expected return. Portfolio X has a
coefficient of variation of 4% ÷ 10% = 0.40, while Portfolio Y has 8% ÷ 12% ≈
0.67. Therefore, Portfolio X has the lower relative variability per unit of
expected return. This does not mean X has the higher absolute return; it means
its risk is lower relative to the return being generated.
4. An insurance portfolio has claim
frequencies that fluctuate considerably from year to year. The actuary
discovers that the average claim frequency is stable, but individual annual
observations vary around that average. Which statistical measure would most
directly quantify the dispersion of annual claim frequencies around their mean?
A. Median B. Conditional probability C.
Expected value D. Variance
Answer: D
Rationale: Variance measures the average squared
deviation of observations from their mean and therefore directly measures
dispersion. The expected value describes the central tendency, while the median
identifies the middle observation after ordering the data. Conditional
probability measures the likelihood of one event given another and does not
measure dispersion. In actuarial experience analysis, understanding both
central tendency and variability is essential when evaluating uncertainty.
5. NIC retains a portion of each
insurance risk but transfers losses above a specified amount to a reinsurer.
What type of reinsurance arrangement is most closely described by this
structure?
A. Proportional quota-share reinsurance B.
Excess-of-loss reinsurance C. Facultative coinsurance arrangement D.
Aggregate premium-sharing arrangement
Answer: B
Rationale: Excess-of-loss reinsurance protects the
insurer against losses exceeding a specified retention, with the reinsurer
covering the amount above that retention subject to the terms of the contract.
Unlike quota-share arrangements, the insurer does not necessarily transfer a
fixed percentage of every loss. This form of reinsurance is particularly useful
for protecting an insurer against large individual claims or defined layers of
loss and can therefore support the management of severity and concentration risk.
6. An actuary develops a model using a
historical dataset and divides the observations into training and validation
samples. What is the primary purpose of the validation sample?
A. To increase the number of historical
observations B. To calculate the insurer's investment income C. To assess how
well the model performs on data not used for fitting D. To guarantee that
future predictions are correct
Answer: C
Rationale: A validation sample provides information
that was not used to fit the model and can therefore help assess how well the
model generalises beyond its fitting data. Good performance on historical
training data alone may result from overfitting, where the model captures noise
or highly specific historical patterns. Validation therefore provides an
important check on model performance, although it cannot guarantee that future
predictions will always be correct.
7. An insurance company receives TZS 100
million today and expects to pay TZS 110 million exactly two years later. If
the annual effective discount rate is 5%, approximately what is the present
value of the future payment?
A. TZS 95.24 million B. TZS 99.77
million C. TZS 104.76 million D. TZS 110.00 million
Answer: B
Rationale: The present value is calculated by
discounting the future payment using the effective annual rate: PV = 110
million ÷ (1.05)². Since (1.05)² = 1.1025, the present value is approximately
TZS 99.77 million. This illustrates why future insurance cash flows cannot be
compared directly with current amounts without considering the time value of
money.
8. NIC observes that the actual number of
claims during the year is substantially higher than the number predicted by its
pricing model. Which actuarial activity would most directly investigate whether
the underlying assumptions remain appropriate?
A. Premium collection B. Investment allocation C.
Asset classification D. Experience analysis
Answer: D
Rationale: Experience analysis compares actual
observed outcomes with expected outcomes derived from actuarial assumptions. If
actual claims materially exceed expected claims, the actuary would investigate
whether claim frequency, severity, exposure characteristics or other
assumptions have changed. This analysis may lead to recommendations for
revising pricing, reserving or risk-management assumptions. It is therefore
directly connected to the stated responsibility of monitoring and managing
NIC's experience.
9. An actuary estimates the probability
of a claim as 0.04 for each of 500 independent policies. What is the expected
number of claims, and what is the variance of the number of claims under a
binomial model?
A. 20 and 19.2 B. 20 and 20.0 C. 24 and
19.2 D. 24 and 24.0
Answer: A
Rationale: For a binomial distribution, the
expected number of claims is np, while the variance is np(1 − p). Here, n = 500
and p = 0.04, giving an expected value of 500 × 0.04 = 20. The variance is 500
× 0.04 × 0.96 = 19.2. The distinction between expected value and variance is
important because the former describes the average outcome while the latter
describes the uncertainty around that average.
10. NIC is considering whether to
transfer part of its insurance risk to another insurer. Which factor would be
most important when assessing the effectiveness of the proposed risk transfer?
A. Whether the arrangement eliminates
every possible future loss B. Whether the contract uses the longest possible
document C. Whether the transferred risk has the highest historical frequency D.
Whether the arrangement genuinely reduces NIC's exposure to the intended risk
Answer: D
Rationale: Effective risk transfer should
materially reduce the insurer's exposure to the risk it intends to manage,
subject to the terms, limits, exclusions and counterparty considerations of the
arrangement. A reinsurance or other risk-transfer arrangement does not need to
eliminate every possible loss to be useful. The actuary should therefore
examine whether the structure actually transfers the intended risk and whether
the remaining exposure is consistent with NIC's risk-management objectives.
11. An actuary calculates the expected
loss from a portfolio as TZS 80 million. The actual loss is TZS 110 million.
Which statement most accurately describes the result?
A. The portfolio has an adverse loss
experience B. The expected loss must equal the actual loss C. The model has
automatically become invalid D. The portfolio has experienced a guaranteed
profit
Answer: A
Rationale: Actual loss exceeding expected loss
represents adverse experience relative to the stated expectation. However, a
single year's adverse result does not automatically prove that the actuarial
model is invalid because random variation is inherent in insurance outcomes.
The actuary should investigate whether the difference is consistent with
expected statistical fluctuation or indicates a change in underlying risk,
assumptions or portfolio characteristics.
12. An insurer applies a deductible of
TZS 500,000 to each eligible claim. A policyholder submits a covered claim of
TZS 2 million. Ignoring other policy conditions, what amount would the insurer
pay?
A. TZS 500,000 B. TZS 1 million C. TZS
1.5 million D. TZS 2 million
Answer: C
Rationale: A deductible is the portion of a covered
loss that remains the policyholder's responsibility before the insurer's
payment begins. Therefore, for a TZS 2 million claim subject to a TZS 500,000
deductible, the insurer would pay TZS 2 million − TZS 500,000 = TZS 1.5
million. The deductible reduces the insurer's payment on each applicable claim
and can also influence claim frequency, policyholder behaviour and expected
claim costs.
13. An actuarial officer receives a
claims dataset in which some records contain missing values for claim amounts.
Before calculating average claim severity, what is the most appropriate first
step?
A. Treat every missing value as zero B.
Replace every missing value with the largest claim C. Ignore the missing
values without investigation D. Determine why the values are missing and
assess an appropriate treatment
Answer: D
Rationale: Missing claim amounts can arise from
different causes, such as incomplete reporting, data-entry problems, claims
still under assessment or system limitations. Treating every missing value as
zero could materially understate severity, while replacing them with arbitrary
values could introduce bias. The actuary should first understand the reason and
pattern of missingness and then determine an appropriate documented treatment
before calculating experience measures.
14. An insurer has 1,000 policies, each
with an annual probability of claim of 0.01. If claim occurrences are
independent, what is the probability that a particular policy has no claim
during the year?
A. 0.01 B. 0.10 C. 0.90 D. 0.99
Answer: D
Rationale: If the probability of a claim is 0.01,
the probability of no claim is its complement: 1 − 0.01 = 0.99. Therefore, a
particular policy has a 99% probability of experiencing no claim during the
year under the stated assumption. The number of policies in the portfolio does
not change the probability for that particular policy, although it would affect
the expected aggregate number of claims.
15. NIC is considering whether a
portfolio's increasing claim severity is caused by inflation or by a change in
the underlying risk profile. Which actuarial technique would be most useful for
investigating the source of the change?
A. Removal of unusually large claims
automatically B. Experience analysis with adjusted assumptions C. Replacement
of all historical observations D. Simple comparison of total premiums
Answer: B
Rationale: Experience analysis allows actual
outcomes to be compared across periods after considering relevant changes in
assumptions and exposure. Adjusting for inflation, exposure changes, claims
development and other relevant factors can help distinguish economic effects
from genuine changes in risk characteristics. Simply comparing total premiums
does not isolate claim-cost drivers, while automatically removing large claims
could distort the true experience and hide important risk information.
16. A portfolio has two risks with
variances of 25 and 36. Their covariance is -10. If equal weights are assigned
to both risks, what is the portfolio variance?
A. 10.25 B. 12.75 C. 15.25 D. 25.50
Answer: A
Rationale: For two equally weighted risks,
portfolio variance is calculated as
(w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2Cov(X,Y)). With both weights equal to
0.5, the calculation is 0.25(25) + 0.25(36) + 2(0.5)(0.5)(−10) = 6.25 + 9 − 5 =
10.25. Therefore, the correct answer is A. The negative covariance reduces the
overall portfolio variance because the two risks do not move perfectly
together.
17. An investment portfolio has a
modified duration of 6 years. If interest rates increase by approximately 1
percentage point, with other factors held constant, what is the approximate
percentage change in the portfolio's value using the duration approximation?
A. An increase of approximately 6% B. A
decrease of approximately 6% C. An increase of approximately 1% D. A decrease
of approximately 1%
Answer: B
Rationale: Modified duration provides an
approximate measure of the percentage change in a bond portfolio's value for a
change in interest rates. Using the approximation ΔV/V ≈ −Duration × Δy, a 1
percentage-point increase in yield with a modified duration of 6 implies an
approximate 6% decrease in value. The relationship is an approximation and is
most useful for relatively small changes in yields, with convexity and other
factors becoming relevant for more precise analysis.
18. A life insurance model assumes a
mortality rate of 0.01 for a particular age group. If 10,000 lives are exposed
to the risk under the same assumption, what is the expected number of deaths?
A. 10 B. 100 C. 1,000 D. 10,000
Answer: B
Rationale: The expected number of deaths is the
number of exposed lives multiplied by the assumed mortality probability: 10,000
× 0.01 = 100. This is an expected value rather than a prediction that exactly
100 deaths will occur. Actual deaths may be higher or lower because of random
variation and differences between the assumed population and the actual
portfolio.
19. An actuary is asked to determine
whether a proposed premium is sufficient to cover expected claims, expenses and
an appropriate margin for risk. Which actuarial function is most directly
involved?
A. Claims settlement B. Investment
custody C. Premium pricing D. Financial auditing
Answer: C
Rationale: Premium pricing involves estimating the
expected cost of future claims and incorporating relevant expenses, risk
margins and other assumptions to determine an appropriate premium. Claims
settlement occurs after losses arise, while investment custody concerns
safeguarding assets. Financial auditing independently examines financial
information but does not itself constitute the actuarial process of determining
an adequate insurance price.
20. An actuarial report recommends
strengthening a particular risk-control process. NIC management accepts the
recommendation and introduces the control. What should the actuarial function
subsequently do to determine whether the recommendation is achieving its
intended purpose?
A. Stop monitoring the risk after
implementation B. Assume implementation guarantees lower losses C. Replace the
recommendation with a new model immediately D. Review relevant outcomes
against the intended objective
Answer: D
Rationale: Implementation of an actuarial
recommendation should be followed by monitoring to determine whether the
intended risk or financial outcome is actually being achieved. This may involve
comparing relevant experience before and after implementation, monitoring key
risk indicators and assessing whether assumptions remain appropriate.
Implementation itself does not guarantee success, so ongoing evaluation is
essential and directly relates to the responsibility of implementing and
monitoring actuarial recommendations.
21. A claim-cost distribution is highly
right-skewed because a small number of claims are extremely large. Which
measure is generally more resistant to the influence of these extreme
observations?
A. Median B. Arithmetic mean C. Total
loss D. Variance
Answer: A
Rationale: The median is less affected by extreme
observations than the arithmetic mean and therefore provides a more robust
measure of central location when a distribution is highly skewed. The mean can
be pulled upward substantially by a small number of very large claims. Variance
is particularly sensitive to extreme observations because deviations are
squared. However, actuaries should not automatically prefer the median for all
purposes because the mean is often essential when estimating expected financial
loss.
22. An insurer has a claim with an
estimated ultimate cost of TZS 10 million. TZS 6 million has already been paid
and the remaining amount is expected to be paid in the future. Ignoring
discounting and further changes in the estimate, what is the outstanding
amount?
A. TZS 10 million B. TZS 6 million C.
TZS 4 million D. TZS 16 million
Answer: C
Rationale: The outstanding amount is the estimated
ultimate claim cost less the amount already paid. Therefore, TZS 10 million −
TZS 6 million = TZS 4 million remains outstanding. This distinction is
important in claims reserving because the ultimate claim cost represents the
expected total cost, while the outstanding amount represents the portion that
has not yet been paid at the valuation date.
23. A risk model gives an estimated
probability of 0.001 for an event in a given year. The event has a potential
financial impact of TZS 5 billion. Which statement best reflects the actuarial
significance of the event?
A. Its expected annual loss is TZS 5
million B. Its expected annual loss is TZS 500 million C. Its expected annual
loss is TZS 50 million D. Its expected annual loss is TZS 500,000
Answer: A
Rationale: Expected loss is calculated as
probability multiplied by loss amount. Thus, 0.001 × TZS 5 billion = TZS 5
million. The calculation does not mean the insurer will actually lose TZS 5
million during the year; it represents the average loss contribution under the
stated probability and severity assumptions. The large potential severity
nevertheless makes the risk important for capital and stress-testing purposes
even though its expected annual loss is relatively small.
24. An actuary observes that two
variables have a correlation coefficient close to zero. Which conclusion is
most appropriate?
A. The variables must be independent B.
The variables must be mutually exclusive C. The variables have no linear
association D. The variables have identical distributions
Answer: C
Rationale: A correlation coefficient close to zero
indicates little or no linear association between the variables. It does not
necessarily prove statistical independence because variables can have nonlinear
relationships while having zero correlation. Mutual exclusivity concerns
whether two events can occur simultaneously and is a different concept.
Likewise, correlation says nothing by itself about whether two variables have
identical distributions.
25. NIC's actuarial team discovers that a
model has produced accurate results historically, but its assumptions are no
longer consistent with current economic and demographic conditions. What is the
most appropriate actuarial response?
A. Continue using the model because
historical accuracy is sufficient B. Ignore current conditions until actual
losses increase C. Review and update relevant assumptions before relying on
projections D. Discard all historical data because assumptions have changed
Answer: C
Rationale: Historical model performance is useful
but does not guarantee that the model remains appropriate when underlying
conditions change. Actuarial projections depend on assumptions about future
conditions, and outdated economic or demographic assumptions can produce
materially misleading results. The appropriate response is therefore to review
the assumptions, assess their continued suitability, update them where
justified, validate the revised model and document the impact. Historical data
should not automatically be discarded because it may remain useful after
appropriate adjustment and interpretation.
26. NIC receives 1,500 motor insurance
claims during a year. Of these, 900 are settled at TZS 400,000 each, while the
remaining 600 are settled at TZS 700,000 each. What is the weighted average
settlement amount per claim?
A. TZS 480,000 B. TZS 520,000 C. TZS
600,000 D. TZS 660,000
Answer: B
Rationale: The total settlement amount is (900 ×
TZS 400,000) + (600 × TZS 700,000) = TZS 360 million + TZS 420 million = TZS
780 million. Dividing the total settlement amount by 1,500 claims gives TZS 780
million ÷ 1,500 = TZS 520,000 per claim. The weighted average is appropriate
because the two claim groups contain different numbers of claims and therefore
cannot simply be averaged without considering their respective frequencies.
27. An insurer's annual claim frequency
has historically averaged 0.08 claims per policy. The portfolio currently
contains 25,000 policies. If the historical frequency remains appropriate, what
is the expected number of claims?
A. 2,000 B. 3,125 C. 20,000 D. 312,500
Answer: A
Rationale: Expected claim frequency is multiplied
by the number of policies to obtain the expected number of claims. Therefore,
25,000 × 0.08 = 2,000 expected claims. The figure is an expected value rather
than a guarantee that exactly 2,000 claims will occur. Actual claims can differ
because of random variation and changes in the underlying risk characteristics
of the portfolio.
28. An insurer reports an increase in
total claim payments during the year. Which additional information would be
most important before concluding that the underlying claim experience has
deteriorated?
A. The colour of the insurer's annual
report B. The number of branches operated by NIC C. Changes in exposure and
portfolio composition D. The number of meetings held by management
Answer: C
Rationale: An increase in total claim payments does
not by itself demonstrate deterioration because the insurer may have
experienced an increase in the number or type of risks insured. Changes in
exposure, portfolio composition, policy mix and other relevant characteristics
can materially affect aggregate claims. Examining these factors allows the
actuary to distinguish an increase caused by greater exposure from a genuine
worsening in the underlying risk experience.
29. An insurer's claim reserve at the
beginning of the year was TZS 300 million. During the year, TZS 220 million was
paid in respect of those claims, and the actuary estimates that TZS 100 million
remains payable. Ignoring other adjustments, what does this experience indicate
about the ultimate claim cost?
A. TZS 200 million B. TZS 300 million C.
TZS 320 million D. TZS 520 million
Answer: C
Rationale: The estimated ultimate cost of the
claims is the amount already paid plus the amount still expected to be paid.
Therefore, TZS 220 million + TZS 100 million = TZS 320 million. Comparing this
estimated ultimate cost with the original TZS 300 million reserve indicates
adverse development of TZS 20 million, assuming the original reserve
represented the expected ultimate cost at the beginning of the year.
30. NIC notices that two insurance
products have identical claim frequencies but substantially different average
claim amounts. What is the most appropriate implication for actuarial analysis?
A. Their expected claim costs must also
be identical B. Their premiums must
necessarily be identical C. Their claim probabilities cannot be compared D. Their
expected claim costs may differ materially because severity differs
Answer: D
Rationale: Identical claim frequencies do not imply
identical expected claim costs because the amount paid when claims occur may
differ substantially. Expected loss depends on both the frequency of claims and
their severity. Therefore, if two products have the same frequency but
materially different average claim amounts, their expected claim costs may
differ significantly, which can affect pricing, reserving and risk assessment.
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