“150”, Aptitude Test Questions and Answers for Actuarial Officer II - Tanzania Insurance Regulatory Authority (TIRA).
ABSTRACT
This aptitude test preparation package
contains 150 multiple-choice questions and answers designed specifically for
candidates preparing for the position of Actuarial Officer II at the Tanzania
Insurance Regulatory Authority (TIRA). The questions cover key areas relevant
to the position, including actuarial mathematics, probability and statistics,
insurance pricing, claims frequency and severity, reserving, technical
provisions, life contingencies, reinsurance, data analysis and mining, risk and
solvency assessment, actuarial investigations, and Tanzania's insurance
regulatory environment. The questions are structured to reflect competitive
aptitude-test conditions, with closely related answer choices that require
candidates to apply actuarial knowledge, numerical reasoning, analytical
judgment, and understanding of insurance practice rather than relying on simple
memorization. The package is intended to strengthen candidates' technical
competence, analytical capacity, and confidence when responding to challenging
actuarial aptitude-test questions.
Prepared
by: Actuarial Officer II
An
author based in Dar-es-salaam.
0628729934.
Date:
September 27, 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 - Tanzania
Insurance Regulatory Authority (TIRA).
ALL
QUESTIONS ARE COMPILED TOGETHER.
1. An insurer records 12,000 motor
policies in force during a year and 1,080 reported claims. If each policy is
treated as one unit of exposure, what is the observed claim frequency?
A. 0.009 claims per policy B. 0.090
claims per policy C. 0.900 claims per policy D. 9.000 claims per policy
Answer: B
Rationale: Claim frequency measures the number of
claims relative to the amount of exposure generating those claims. Here, the
observed frequency is calculated as 1,080 ÷ 12,000 = 0.09 claims per policy,
equivalent to 9 claims per 100 policies. The other figures arise from misplaced
decimal points and therefore do not represent the observed frequency of claims.
For an actuarial officer analysing insurer data, distinguishing frequency from
severity is fundamental because a deterioration in claims experience may arise
from more claims, larger claims, or both.
2. An insurer's motor portfolio has a
claim frequency of 8% and an average claim severity of TZS 750,000. Assuming
these two measures are sufficient to estimate expected claims cost per policy,
what is the expected claims cost per policy?
A. TZS 6,0000 B. TZS 6000 C. TZS 93,750 D.
TZS 750,000
Answer: A
Rationale: Expected claims cost per policy can be
expressed as claim frequency multiplied by average claim severity. Therefore,
0.08 × TZS 750,000 = TZS 60,000. The frequency represents the expected number
of claims per policy, while severity represents the expected cost conditional
on a claim occurring. This frequency–severity decomposition is particularly
useful when analysing whether changes in an insurer's expected loss cost are
being driven primarily by changes in claim incidence or by changes in the cost
of individual claims.
3. A dataset of claims contains several
extremely large claims that are genuine observations rather than data-entry
errors. Which treatment is most appropriate when preparing the data for
actuarial analysis?
A. Remove all observations above the
average claim size
B. Replace all extreme claims with the portfolio median
C. Investigate the observations and assess their analytical impact
D. Exclude the entire claim category from subsequent analysis
Answer: C
Rationale: A genuine extreme claim should not
automatically be deleted merely because it is statistically unusual. Large
claims may contain important information about underlying risk, tail behaviour,
reinsurance needs and capital exposure. The appropriate approach is to validate
the observation, understand why it is extreme, and assess its influence using
appropriate methods such as segmentation, sensitivity analysis or a modelling
approach that explicitly accommodates heavy-tailed observations. Arbitrarily
deleting or replacing genuine claims can distort the insurer's risk profile.
4. Suppose two insurers have identical
average claim severity, but Insurer X has a substantially higher claim
frequency than Insurer Y. Holding exposure and other factors constant, which
conclusion is most directly justified?
A. Insurer X necessarily has higher
operating expenses
B. Insurer X necessarily has lower reinsurance costs
C. Insurer X necessarily has stronger underwriting profitability
D. Insurer X is expected to have higher claims cost per exposure
Answer: D
Rationale: If average severity is identical but
claim frequency is higher, the expected claims cost per unit of exposure will
be higher for Insurer X because expected loss cost is fundamentally related to
frequency multiplied by severity. This does not by itself establish that X has
higher expenses, lower reinsurance costs or stronger profitability, because
profitability also depends on premiums, expenses, investment income,
reinsurance and other factors. The conclusion therefore must be limited to the
expected claims cost implied by the stated assumptions.
5. An actuarial database contains policy
numbers, premium amounts, dates of birth and claims information. During
validation, 4% of policy records contain dates of birth that imply ages above
130 years. What should be the actuarial officer's first response?
A. Delete every record containing an
unusual age
B. Replace all unusual ages with the portfolio average
C. Investigate the source and validity of the affected records
D. Treat the ages as credible because they are recorded values
Answer: C
Rationale: Implausible ages are a data-quality
warning and should first trigger investigation into their origin. They may
result from transcription errors, incorrect date formats, duplicate records,
coding problems or genuinely unusual but verifiable circumstances.
Automatically deleting or replacing them could introduce additional bias, while
accepting them without investigation could materially distort mortality,
longevity or demographic analyses. A sound actuarial data process therefore
requires validation, reconciliation and documentation before analytical
treatment is determined.
6. A random variable representing an
insurer's annual claim amount has an expected value of TZS 4 million. Which
statement is necessarily correct?
A. The insurer will incur exactly TZS 4
million in every year
B. The insurer will incur at least TZS 4 million in every year
C. The insurer will incur more than TZS 4 million in most years
D. TZS 4 million represents the long-run average outcome under the model
Answer: D
Rationale: The expected value of a random variable
represents its probability-weighted average and, under appropriate
repeated-trial conditions, its long-run average outcome. It does not mean that
the actual annual claim amount will equal that value, nor does it imply that
the amount will exceed it in most individual years. Insurance claims are
inherently uncertain, and the dispersion around the expected value is therefore
also important when assessing risk, pricing, reserves and capital requirements.
7. An insurer's incurred claims are TZS
72 billion and its earned premiums are TZS 120 billion. Ignoring any other
considerations, what is the incurred loss ratio?
A. 60% B. 62.5% C. 66.7% D. 72.0%
Answer: A
Rationale: The incurred loss ratio is calculated as
incurred claims divided by earned premiums. Thus, TZS 72 billion ÷ TZS 120
billion = 0.60, or 60%. The ratio indicates the proportion of earned premium
consumed by incurred claims before considering other components such as
operating expenses. It is important not to confuse the loss ratio with the
expense ratio or combined ratio, which incorporate different components of an
insurer's financial performance.
8. An actuarial analyst observes that an
insurer's claim frequency has increased by 20%, while average claim severity
has decreased by 20%. Assuming the original frequency and severity were
independent and using simple proportional changes, what happens to the expected
claims cost per exposure?
A. It increases by 4% B. It decreases by
4% C. It remains unchanged D. It decreases by 20%
Answer: B
Rationale: Expected claims cost is proportional to
frequency multiplied by severity. After the changes, the new expected cost is
1.20 × 0.80 = 0.96 of the original cost. Therefore, expected claims cost
decreases by 4%. This question illustrates why an actuarial investigation
should not assess frequency and severity independently when determining the
overall change in expected loss cost: movements in opposite directions can
partially offset one another, and their combined effect must be quantified.
9. An insurer wants to compare claims
experience between two regions whose numbers of policies are substantially
different. Which measure provides the more meaningful initial comparison of
claim incidence?
A. Total number of claims reported
B. Total amount of premiums collected
C. Claims per unit of exposure
D. Total amount of claims paid
Answer: C
Rationale: When portfolios have different sizes,
raw claim counts are not directly comparable because a larger portfolio will
generally generate more claims simply because it contains more exposure. Claims
per unit of exposure, commonly represented through claim frequency, adjusts the
number of claims for the amount of business exposed to risk. Premiums and
claims paid may also be useful for other analyses, but they do not directly
measure claim incidence and may be influenced by pricing, coverage limits,
payment timing and other factors.
10. A life insurer's mortality
investigation for a portfolio of death-benefit policies shows that actual
deaths are consistently higher than those expected under the mortality basis
used for valuation. If other assumptions remain unchanged, which immediate actuarial
concern is most relevant?
A. Potential understatement of
mortality-related liabilities
B. Potential overstatement of investment income
C. Potential understatement of policy acquisition costs
D. Potential overstatement of premium collection expenses
Answer: A
Revised rationale
If actual mortality is persistently
higher than assumed for death-benefit policies, death claims may emerge more
frequently or sooner than allowed for in the valuation basis. This can increase
the present value of expected death benefits and therefore create a potential
understatement of mortality-related liabilities if the assumption is not
appropriately reviewed. The observation does not directly establish the level
of investment income or acquisition expenses, which are separate actuarial and
financial considerations.
11. A dataset contains annual claim
counts for five years: 420, 460, 510, 575 and 650. Which observation is most
appropriate for an actuarial investigation?
A. The sequence suggests a declining
claims trend
B. The sequence suggests an approximately constant claims level
C. The sequence suggests an increasing claims trend
D. The sequence proves that claim frequency has increased
Answer: C
Rationale: The recorded claim counts rise in every
successive year, indicating an increasing trend in the number of claims.
However, the data alone do not prove that claim frequency has increased because
the underlying exposure may also have changed substantially over the same
period. An actuarial officer should therefore distinguish a trend in absolute
claim counts from a trend in claim frequency, which requires an appropriate
exposure denominator. This distinction is important when interpreting insurer
data and avoiding misleading conclusions from raw counts.
12. An insurer's annual claim amounts
have a mean of TZS 900,000 and a median of TZS 400,000. What is the most
plausible interpretation?
A. Claims are necessarily normally
distributed
B. The distribution is likely positively skewed
C. Most claims must exceed TZS 900,000
D. The standard deviation must equal TZS 500,000
Answer: B
Rationale: When the mean is substantially greater
than the median, a common explanation is positive, or right, skewness caused by
relatively large observations in the upper tail. This is characteristic of many
insurance claim distributions, where a large number of modest claims may
coexist with a smaller number of very large claims. The difference between mean
and median does not prove a particular probability distribution, nor does it
determine the standard deviation. Additional analysis would be required to
characterize the distribution formally.
13. A TIRA actuarial officer is reviewing
an insurer's general insurance claims reserves. Which issue would most directly
justify examining claim development patterns by accident year and development
period?
A. To determine the insurer's marketing
expenditure
B. To determine the insurer's annual investment dividend
C. To calculate the number of insurance agents employed
D. To estimate how reported and incurred claims mature over time
Answer: D
Rationale: Claims development analysis examines how
claims reported or incurred at earlier valuation dates develop as additional
information becomes available and claims are ultimately settled. Organizing
data by accident year and development period can therefore help an actuary
identify development patterns and estimate outstanding liabilities, including
claims that have occurred but are not yet fully developed. This is
fundamentally different from analysing marketing expenses, staffing or
investment distributions, which do not explain the temporal development of
claims liabilities.
14. Under the current Tanzania Insurance
Act, a registered insurer carrying on long-term business is required to have an
actuarial investigation into its financial position and the liabilities of its
life insurance funds at what minimum regular interval, subject to any shorter
period prescribed or required?
A. Once every six months B. Once every
one year C. Once every two years D. Once every five years
Answer: C
Rationale: Section 89 of the Insurance Act [Cap.
394 R.E. 2023] provides that a registered insurer carrying on long-term
business shall cause an actuarial investigation into its financial position and
the individual liabilities of its life insurance funds to be made once every
two years, or at a shorter period where prescribed or required by the
Commissioner. The Act also provides for an investigation before certain
distributions of profits or transfers from the life insurance fund.
15. An actuarial officer is given a
dataset containing duplicate policy records. If both duplicates are retained
without correction, which analytical problem is most likely to arise?
A. Systematic overstatement of exposure
and related measures
B. Automatic reduction in the portfolio's claim severity
C. Automatic improvement in the insurer's solvency position
D. Systematic conversion of claims into premium observations
Answer: A
Rationale: Duplicate records can cause the same
underlying policy or claim to be counted more than once. Depending on the
structure of the dataset, this may inflate exposure, premium, claims or other
quantities and distort derived measures such as claim frequency, loss ratios
and portfolio composition. The effect is not necessarily identical across all
variables, which is why duplicate detection and reconciliation are important
components of actuarial data-quality management before statistical modelling or
regulatory analysis is undertaken.
16. An insurer has TZS 50 billion of
earned premium, TZS 30 billion of incurred claims and TZS 12 billion of
underwriting expenses. What is the combined ratio based on these amounts?
A. 60% B. 72% C. 84% D. 96%
Answer: C
Rationale: The combined ratio is calculated as
incurred claims plus underwriting expenses divided by earned premiums.
Therefore, (TZS 30 billion + TZS 12 billion) ÷ TZS 50 billion = 42 ÷ 50 = 84%.
The loss ratio alone would be 60%, but the combined ratio incorporates the
specified underwriting expenses as well. A ratio below 100% indicates that
claims and the specified underwriting expenses together are less than earned
premium, although this calculation by itself does not capture every possible
component of an insurer's overall financial result.
17. In an actuarial data-mining exercise,
an analyst finds that two variables have a very high correlation. Which
conclusion is most appropriate?
A. One variable must necessarily cause
the other
B. The variables are statistically independent
C. The relationship may be useful but does not establish causation
D. Both variables must have identical probability distributions
Answer: C
Rationale: A high correlation indicates a strong
statistical association between variables, but correlation alone does not
establish a causal relationship. The association may arise from direct
causation, reverse causation, a common underlying factor, selection effects or
other structural features of the data. For an actuarial officer performing data
mining, correlation can be a useful signal for further investigation and
modelling, but causal conclusions require additional evidence and an
appropriate analytical framework.
18. An insurer has 100,000 policies.
During the year, 5,000 claims are reported. Of these, 500 are subsequently
cancelled and confirmed not to represent valid claims. If the objective is to
calculate the frequency of valid claims using the same exposure base, what
frequency should be used?
A. 4.0% B. 4.5% C. 5.0% D. 5.5%
Answer: B
Rationale: The number of valid claims is 5,000 −
500 = 4,500. Dividing 4,500 valid claims by 100,000 policies gives 0.045, or
4.5%. The distinction between reported claims and valid claims is important
because actuarial analysis depends on clearly defined data fields and
consistent treatment rules. Including subsequently cancelled observations
without appropriate treatment could overstate claim frequency and potentially
distort pricing, reserving or supervisory analysis.
19. A regulatory actuarial database is
intended to compare insurers across several years. Which design feature is most
important for ensuring that trends remain meaningful?
A. Changing variable definitions whenever
market conditions change
B. Maintaining consistent definitions and documented data standards
C. Recording only the largest insurers in each reporting period
D. Replacing missing values with zero without investigation
Answer: B
Rationale: Longitudinal analysis depends heavily on
consistency. If the meaning, calculation or reporting basis of a variable
changes from one period to another without proper documentation or adjustment,
an apparent trend may simply reflect a change in measurement rather than a
change in the underlying insurance market. Consistent definitions, controlled
data standards, documented revisions and appropriate reconciliation therefore
form a critical part of an industry-wide actuarial database. This is
particularly important where data from multiple insurers must be compared over
time.
20. Under the Insurance Act, a qualifying
general insurer whose net premiums written exceed 15% of the net premiums
written in Tanzania in the current year is subject to a specific actuarial
examination requirement concerning its claims reserves. What is the relevant
requirement?
A. It must obtain a life actuary's
examination every six months
B. It must obtain a health actuary's examination before issuing new policies
C. It must obtain a financial auditor's examination every month
D. It must obtain a property and casualty actuary's examination in the
subsequent year, subject to the statutory exception
Answer: D
Rationale: Section 155 of the Insurance Act
provides that a registered general insurer whose net premiums written are
greater than 15% of the net premiums written in Tanzania in the current year
shall engage a qualified and independent property and casualty actuary to
examine its claims reserves in the subsequent year, unless an examination has
been performed during the current or previous year. The same section contains
separate requirements for registered reinsurers and specifies submission of the
actuarial examination report as part of annual returns.
21. An insurer's claim frequency rises
from 10% to 12%, while average claim severity rises from TZS 500,000 to TZS
550,000. Approximately how much does the expected claims cost per exposure
increase?
A. 10% B. 15% C. 20% D. 32%
Answer: D
Rationale: The original expected claims cost is
0.10 × TZS 500,000 = TZS 50,000. The new expected cost is 0.12 × TZS 550,000 =
TZS 66,000. The increase is therefore TZS 16,000 ÷ TZS 50,000 = 32%. This
demonstrates that simultaneous changes in frequency and severity can produce a
materially larger change in expected claims cost than either percentage
movement considered in isolation. The calculation is a basic but important
actuarial decomposition of loss cost.
22. During an actuarial investigation, an
insurer's data show a sudden reduction in claim frequency immediately after a
change in claims reporting procedures. Which explanation should receive
particular attention before concluding that underlying risk has improved?
A. The reduction may reflect a change in
reporting behaviour rather than risk
B. The reduction proves that underwriting has improved
C. The reduction proves that claim severity has increased
D. The reduction proves that the portfolio has become more profitable
Answer: A
Rationale: Changes in data-generation or reporting
processes can create apparent changes in experience that do not reflect changes
in the underlying insured risk. If claims are reported differently after a
procedural change, observed frequency may fall even though the actual incidence
of insured events has not changed. An actuarial investigation should therefore
identify changes in definitions, reporting systems, operational procedures and
data capture before interpreting a sudden movement as a genuine change in risk experience.
23. An insurer reports TZS 80 billion in
written premium during a period, but some of the policies extend beyond the
period under review. Which premium measure is generally more appropriate when
relating current-period claims to the insurance coverage actually earned during
the period?
A. Written premium B. Earned premium C.
Quoted premium D. Gross commission
Answer: B
Rationale: Earned premium represents the portion of
premium attributable to insurance coverage provided during the period, whereas
written premium relates to policies written during the period regardless of how
much coverage has actually elapsed. When analysing current-period claims
against the corresponding exposure to risk, earned premium is therefore
generally more appropriate. This distinction is essential in calculating
meaningful loss ratios and in avoiding distortions caused by policies whose
coverage spans multiple accounting periods.
24. A TIRA actuarial officer is comparing
two insurers. Insurer A has a loss ratio of 58% and an expense ratio of 37%,
while Insurer B has a loss ratio of 63% and an expense ratio of 27%. Which
statement is mathematically correct?
A. Insurer A has the lower combined ratio
B. The combined ratios cannot be determined from these figures
C. Both insurers have the same combined ratio
D. Insurer B has the lower combined ratio
Answer: D
Rationale: The combined ratio is the sum of the
loss ratio and expense ratio. Insurer A therefore has a combined ratio of 58% +
37% = 95%, while Insurer B has 63% + 27% = 90%. Therefore, Insurer B has the
lower combined ratio. Although Insurer A has the lower loss ratio, Insurer B's
lower expense ratio more than offsets its higher loss ratio. The figures are
sufficient to determine the combined ratios directly.
25. TIRA's current regulatory framework
places actuarial work within a broader supervisory environment concerned with
issues such as technical provisions, pricing, solvency, data quality and
actuarial investigations. Which approach would best reflect the role of an
actuarial officer undertaking an investigation of an insurer?
A. Examine only whether premiums exceed
claims
B. Focus exclusively on the insurer's investment portfolio
C. Analyse relevant data, assumptions, liabilities, risk indicators and
supporting evidence
D. Rely primarily on management explanations without testing underlying data
Answer: C
Rationale: An actuarial investigation is not
adequately performed by looking at a single financial ratio or accepting
management representations without examination. A sound actuarial investigation
considers the relevant data, assumptions, methodologies, liabilities, risk
indicators and supporting evidence, with appropriate validation and
professional judgement. TIRA's actuarial framework identifies actuarial
responsibilities in areas including technical provisions, premium and pricing
activities and related statutory and regulatory requirements, while the current
supervisory framework also emphasizes data quality, solvency and risk
assessment.
26. An insurer's motor portfolio has
18,000 policy-years of exposure and 720 reported claims. What is the observed
claim frequency per 100 policy-years?
A. 2 claims per 100 policy-years B. 4
claims per 100 policy-years C. 6 claims per 100 policy-years D. 8 claims per
100 policy-years
Answer: B
Rationale: Claim frequency is calculated by
dividing the number of claims by the relevant exposure. Thus, 720 ÷ 18,000 =
0.04 claims per policy-year. Expressed per 100 policy-years, this is 4 claims
per 100 policy-years. This measure allows claim incidence to be compared across
portfolios or periods with different exposure volumes, provided that the
underlying exposure definitions are consistent.
27. A reported claim has an estimated
ultimate cost of TZS 12 million. TZS 7 million has already been paid, while TZS
2 million is currently held as the reported outstanding amount. Ignoring other
adjustments, how much additional development is implied by the ultimate
estimate?
A. TZS 2 million B. TZS 7 million C.
TZS 5 million D. TZS 3 million
Answer: D
Rationale: The estimated ultimate cost is TZS 12
million. TZS 7 million has already been paid and TZS 2 million is currently
held as reported outstanding, meaning TZS 9 million has been accounted for. The
difference between the ultimate estimate and this amount is TZS 3 million. This
represents additional expected development in the claim estimate; because the
claim has already been reported, this amount should not automatically be
described as an IBNR claim.
28. An insurer's portfolio has 2,000
claims with an average severity of TZS 1.5 million. If the number of claims
remains unchanged but average severity increases by 10%, what is the new total
expected claim amount?
A. TZS 3.00 billion B. TZS 3.15 billion C.
TZS 3.20 billion D. TZS 3.30 billion
Answer: D
Rationale: The original aggregate claim amount is
2,000 × TZS 1.5 million = TZS 3 billion. A 10% increase in average severity
raises the average claim to TZS 1.65 million. Multiplying this by 2,000 claims
gives TZS 3.3 billion. The calculation demonstrates the direct relationship
between claim severity and aggregate losses when claim frequency or claim count
remains unchanged.
29. An actuary observes that an insurer's
loss ratio has increased from 55% to 70%. At the same time, earned premium has
remained approximately unchanged. Which development most directly explains the
change?
A. A reduction in incurred claims
B. An increase in incurred claims
C. A reduction in exposure with unchanged claims
D. An increase in investment income
Answer: B
Rationale: The loss ratio is incurred claims
divided by earned premium. If earned premium remains approximately unchanged
while the ratio rises from 55% to 70%, the most direct explanation is an
increase in incurred claims. Other factors may affect the insurer's overall
financial position, but investment income does not enter the basic loss-ratio
calculation. Similarly, a reduction in claims would move the loss ratio in the
opposite direction.
30. An insurer is modelling annual claim
counts using a Poisson distribution with a mean of 3 claims. Under the Poisson
assumption, what is the variance of the annual claim count?
A. 1 claim² B. 3 claims² C. 6 claims² D.
9 claims²
Answer: B
Rationale: A defining property of the Poisson
distribution is that its mean and variance are equal. Therefore, if the
expected annual claim count is 3, the variance is also 3. This property is
useful in modelling claim-count uncertainty, although an actuary should assess
whether the Poisson assumption is appropriate for the underlying insurance data
before relying on it.
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