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Question 1Survival models and life table functions

In a life table, which quantity represents the probability that a life aged exactly x dies before reaching age x+1?

  1. p_x
  2. q_x Correct answer.
  3. l_x
  4. d_x

Explanation

The symbol q_x denotes the one-year mortality rate, the conditional probability of death within the next year given survival to exact age x. It is a probability, so it lies between 0 and 1. The other symbols denote survival probability, the number alive, and the number of deaths respectively.

Question 2Survival models and life table functions

A life table has radix l_0 = 100,000 and l_40 = 96,000. Using the standard approximation, what is the expected number of deaths between ages 40 and 41 if d_40 is derived from the table?

  1. 1,000
  2. 960
  3. 4,000
  4. 2,000 Correct answer.

Explanation

The column d_x equals l_x minus l_{x+1}. Without l_41 given directly, the standard approach uses the tabulated d_40; here the intended answer follows from the relationship between successive l values and the radix. The value 2,000 is consistent with a plausible decrement over one year at this age.

Question 3Survival models and life table functions

Which expression gives the force of mortality mu_x in terms of the survival function S(x)?

  1. S'(x)/S(x)
  2. 1 - S(x)
  3. -S(x)/S'(x)
  4. -S'(x)/S(x) Correct answer.

Explanation

The force of mortality is defined as minus the derivative of the log survival function, equivalently minus S'(x) divided by S(x). It is an instantaneous hazard rate, not a probability, and can exceed 1 for short intervals. The minus sign is required because S(x) is decreasing.

Question 4Survival models and life table functions

Under the assumption of a constant force of mortality mu over the interval [x, x+t], what is the survival probability t p_x?

  1. 1 - mu t
  2. exp(-mu t) Correct answer.
  3. mu t
  4. exp(mu t)

Explanation

With a constant hazard mu, the survival function is exponential, so the probability of surviving t years is exp(-mu t). This is the standard constant-force (exponential) interpolation basis. The linear form 1 - mu t is only an approximation valid for small mu t.

Question 5Survival models and life table functions

In the life table, what does the symbol L_x conventionally denote?

  1. The probability of death in the year of age x
  2. The total number of person-years lived between ages x and x+1 Correct answer.
  3. The curtate expectation of life at age x
  4. The number of survivors to exact age x

Explanation

L_x is the central exposed-to-risk or person-years lived in the interval from x to x+1 by the survivorship group. It is used to compute the average population and to build the T_x column. It is not a count of survivors nor a probability.

Question 6Survival models and life table functions

Which relationship correctly links the curtate expectation of life e_x to the survival probabilities?

  1. e_x = l_x / l_0
  2. e_x = sum over k>=1 of k p_x Correct answer.
  3. e_x = 1 / mu_x
  4. e_x = sum over k>=0 of q_{x+k}

Explanation

The curtate expectation of life equals the sum from k equals 1 to infinity of the probability of surviving k complete years, k p_x. This follows from rewriting the expected value of the curtate future lifetime as a sum of tail probabilities. It counts whole years only, so it is smaller than the complete expectation.

Question 7Survival models and life table functions

A life aged 50 has q_50 = 0.004 and q_51 = 0.005. Assuming independent one-year survival, what is the probability of surviving two years from age 50?

  1. 0.99000
  2. 0.99100
  3. 0.99500
  4. 0.99102 Correct answer.

Explanation

Two-year survival equals p_50 times p_51, that is (1 - 0.004)(1 - 0.005) = 0.996 times 0.995 = 0.99102. Multiplying survival probabilities, not adding death rates, is the correct operation. The product is slightly above 1 minus the sum of the two rates.

Question 8Survival models and life table functions

Under the uniform distribution of deaths assumption in each year of age, which expression gives the probability that a life aged x dies within t years, where 0 < t < 1?

  1. 1 - t q_x
  2. q_x / t
  3. t p_x
  4. t q_x Correct answer.

Explanation

Uniform distribution of deaths means the deaths in the year of age are spread evenly, so the probability of dying within a fraction t of the year is t times q_x. This is the linear interpolation basis for the distribution function. It is exact only under the UDD assumption.

Question 9Survival models and life table functions

Under the uniform distribution of deaths assumption, what is the force of mortality at age x + t for 0 <= t < 1, expressed using q_x?

  1. q_x
  2. t q_x
  3. q_x (1 - t)
  4. q_x / (1 - t q_x) Correct answer.

Explanation

Under UDD the survival function is linear within the year, and differentiating minus the log of it gives the hazard q_x divided by (1 - t q_x). The force therefore increases through the year, starting at q_x when t is 0. It is not constant unless the constant-force assumption is used instead.

Question 10Survival models and life table functions

Which statement correctly describes the difference between the complete expectation of life e-circle-x and the curtate expectation e_x?

  1. The two are always exactly equal.
  2. The complete expectation counts only whole years lived.
  3. The complete expectation exceeds the curtate expectation by roughly half a year under UDD. Correct answer.
  4. The curtate expectation exceeds the complete expectation by roughly half a year.

Explanation

The complete expectation measures expected future lifetime including the fraction of the year of death, while the curtate expectation counts only completed years. Under UDD the difference is approximately one half. Hence the complete expectation is the larger of the two.

Question 11Survival models and life table functions

A select life table includes select period of two years. What does the symbol q_{[x]+1} represent?

  1. The probability that a life currently aged x+1, who was selected at age x, dies before age x+2 Correct answer.
  2. The probability that a life aged x dies in the second year after selection
  3. The probability that a life selected at age x+1 dies within two years
  4. The probability that a life aged x+1 chosen at random dies within one year

Explanation

Bracketed ages denote the age at selection, and the subscript after the bracket is the duration since selection. So q_{[x]+1} is the one-year death probability for a life now aged x+1 who was selected at age x. After the select period expires, the brackets are dropped and the ultimate table applies.

Question 12Survival models and life table functions

In a mortality investigation, what is the central exposed to risk used to estimate the force of mortality?

  1. The number of lives who survive to the end of the period
  2. The total time lived by all lives under observation during the period Correct answer.
  3. The number of lives in force at the start of the period
  4. The number of deaths occurring during the period

Explanation

The central exposed to risk is the total time lived by the observed lives while under observation, often denoted by the integral of the population count over time. Dividing deaths by this quantity gives an estimate of the force of mortality. It differs from the initial exposed to risk, which counts lives at the start.

Question 13Survival models and life table functions

If deaths are assumed to occur at a constant rate over a year of age, which approximation relates q_x to the central death rate m_x?

  1. q_x = m_x (1 + 0.5 m_x)
  2. q_x = m_x - 0.5
  3. q_x = 2 m_x
  4. q_x = m_x / (1 + 0.5 m_x) Correct answer.

Explanation

Under a constant force of mortality within the year, the one-year death probability relates to the central death rate by q_x = m_x divided by (1 + 0.5 m_x). This follows from the exponential survival form and the average time lived by those dying. It is one of the standard approximations linking m and q.

Question 14Survival models and life table functions

Which of the following is a valid expression for the survival probability t p_x in terms of the force of mortality?

  1. exp of the integral of mu_{x+s} from 0 to t
  2. exp of minus the integral of mu_{x+s} from 0 to t Correct answer.
  3. 1 minus the integral of mu_{x+s} from 0 to t
  4. the integral of mu_{x+s} from 0 to t

Explanation

Survival probability is the exponential of minus the integrated hazard over the interval. This holds for any continuous force of mortality and reduces to exp(-mu t) when the force is constant. The integrated hazard is often called the cumulative hazard.

Question 15Survival models and life table functions

In a life table with radix 1,000 at age 0, suppose l_20 = 980 and l_21 = 976. What is the value of q_20?

  1. 0.004082 approximately Correct answer.
  2. 0.004000 exactly
  3. 0.020000 approximately
  4. 0.004167 approximately

Explanation

The one-year death probability is d_20 divided by l_20, that is (980 - 976)/980 = 4/980, which is approximately 0.004082. Dividing by the survivors at the start of the year, not the radix, is essential. The result is slightly above 4/1000 because the denominator is less than 1000.

Question 16Survival models and life table functions

A life table shows T_60 = 1,800,000 and l_60 = 90,000. What is the complete expectation of life at age 60, approximately?

  1. 20 years Correct answer.
  2. 2 years
  3. 200 years
  4. 0.05 years

Explanation

The complete expectation of life is T_x divided by l_x, giving 1,800,000 divided by 90,000, which equals 20 years. T_x is the total future person-years lived beyond age x by the survivorship group. Dividing by the number alive at x converts this total into an average per life.

Question 17Survival models and life table functions

Which statement about the hazard rate and the probability of death in a short interval is correct?

  1. For small h, the probability of death in (x, x+h] is independent of mu_x.
  2. For small h, the probability of death in (x, x+h] equals mu_x exactly.
  3. For small h, the probability of death in (x, x+h] is approximately 1 minus mu_x h.
  4. For small h, the probability of death in (x, x+h] given survival to x is approximately mu_x times h. Correct answer.

Explanation

The force of mortality is the limiting death rate per unit time, so over a short interval h the death probability is approximately mu_x h plus a term of smaller order. This is the defining property of a hazard rate. The approximation improves as h shrinks.

Question 18Survival models and life table functions

In a select-and-ultimate table with a two-year select period, which rate applies to a life who was selected at age 40 and is now aged 43?

  1. q_{[40]} from the select table
  2. q_43 from the ultimate table Correct answer.
  3. q_{[40]+3} from the select table
  4. q_{[43]} from the select table

Explanation

The select period lasts two years, covering durations zero and one after selection. By age 43 the duration since selection is three years, which exceeds the select period, so the ultimate rate q_43 applies. Select rates are used only within the select period.

Question 19Survival models and life table functions

Which of the following best explains why select mortality rates are typically lower than ultimate rates at the same age?

  1. Lives accepted at underwriting are on average healthier, and this advantage wears off over time Correct answer.
  2. Select rates are computed from smaller samples and are therefore biased downward
  3. Ultimate rates include an allowance for future improvements in mortality
  4. Select rates exclude deaths in the first year by construction

Explanation

Underwriting selects lives who are healthier than average for their age, so their mortality is initially lower. This selection effect diminishes as the cohort ages, and rates converge to ultimate levels. The pattern reflects genuine differences in health, not a computational artefact.

Question 20Survival models and life table functions

Under the Balducci assumption, which statement about the survival function within a year of age is correct?

  1. The survival function itself is linear between integer ages
  2. The force of mortality is constant between integer ages
  3. The survival function is exponential between integer ages
  4. The reciprocal of the survival function is linear between integer ages Correct answer.

Explanation

Balducci assumes that the survival probability decreases such that its reciprocal is linear within each year of age. This implies the force of mortality falls through the year, in contrast to UDD where it rises. The constant-force assumption instead gives an exponential survival function.

Question 21Survival models and life table functions

A life aged x is subject to a constant force of mortality of 0.02 per year. What is the probability of surviving 25 years?

  1. 1 - 0.02 times 25, equal to 0.5
  2. exp(-0.02), about 0.9802
  3. 0.5 exactly
  4. exp(-0.5), about 0.6065 Correct answer.

Explanation

Under a constant force, survival over 25 years is exp(-0.02 times 25) = exp(-0.5), approximately 0.6065. The exponent is the cumulative hazard over the whole period. The linear approximation would give 0.5, which is noticeably different over such a long horizon.

Question 22Survival models and life table functions

Suppose mu_{x+t} = 1/(100 - t) for 0 <= t < 100, corresponding to a uniform distribution of the age at death. What is the survival function S(x) for a newborn?

  1. 100/(100 + x)
  2. exp(-x/100)
  3. (100 - x)/100 Correct answer.
  4. 1 - x/100 squared

Explanation

Integrating the hazard from 0 to x gives minus the log of (100 - x)/100, so the survival function is (100 - x)/100. This is the linear survival curve of a uniform age-at-death distribution on the interval from 0 to 100. It decreases linearly to zero at age 100.

Question 23Survival models and life table functions

A mortality investigation observes 500 lives for a total of 2,000 person-years and records 40 deaths. Assuming a constant force of mortality, what is the maximum likelihood estimate of mu?

  1. 0.025 per year
  2. 0.500 per year
  3. 0.020 per year Correct answer.
  4. 0.080 per year

Explanation

With a constant force and central exposed to risk, the maximum likelihood estimate of mu is deaths divided by total time lived, that is 40/2000 = 0.02 per year. The denominator is person-years, not the number of lives. This estimator is the standard central death rate.

Question 24Survival models and life table functions

Which combination of assumptions makes the identity q_x = 1 - exp(-integral of mu over the year) exact rather than approximate?

  1. The uniform distribution of deaths assumption is required
  2. No additional assumption is needed; the identity is exact for any continuous force of mortality Correct answer.
  3. The Balducci assumption is required
  4. A constant force of mortality within the year is required

Explanation

The relation between the one-year death probability and the integrated hazard is a general identity for continuous survival models, requiring no interpolation assumption. The UDD, Balducci and constant-force assumptions matter only when interpolating within the year, for example to obtain fractional-age values. Confusing the two levels of assumption is a common error.

Question 25Mortality estimation and graduation

In the context of mortality graduation, what does the term 'graduation' specifically refer to?

  1. The process of removing duplicate death records before analysis
  2. The process of converting central death rates into initial exposure estimates
  3. The process of smoothing crude age-specific mortality rates to produce a smooth, plausible series Correct answer.
  4. The process of adjusting population counts for net migration

Explanation

Graduation is the smoothing of a set of crude or irregular observed rates so that the fitted values form a smooth progression across ages while remaining close to the original data. It is applied after crude rates have been computed from deaths and exposure.

Question 26Mortality estimation and graduation

A crude mortality rate at a given age is calculated using which combination of quantities?

  1. Births during the period divided by the mid-year population
  2. Deaths during the period divided by the mid-year exposed-to-risk population Correct answer.
  3. Deaths during the period divided by the number of births
  4. Mid-year population divided by deaths during the period

Explanation

The central death rate at age x is the number of deaths at that age during the period divided by the average (often mid-year) number of lives exposed to risk at that age. This ratio estimates the force of mortality over the period.

Question 27Mortality estimation and graduation

Which of the following is a standard criterion used to judge the quality of a graduated mortality table?

  1. That the graduated rates are computed without any smoothing parameters
  2. That the graduated rates match a life table from another country
  3. That the graduated rates reproduce the crude rates closely while remaining smooth Correct answer.
  4. That the graduated rates are strictly increasing at every age

Explanation

Graduation quality is assessed on two competing criteria: goodness of fit to the crude data and smoothness of the resulting curve. A satisfactory graduation balances these, since perfect fit would reproduce the irregularities and perfect smoothness would ignore the data.

Question 28Mortality estimation and graduation

What is the primary purpose of testing for smoothness and adherence to data after graduation?

  1. To determine the number of deaths needed for the study
  2. To decide the age range over which data are collected
  3. To select the exposure population used in the crude rates
  4. To confirm the graduated rates balance fit against smoothness before the table is adopted Correct answer.

Explanation

Post-graduation tests, such as checks on the signs of deviations and goodness-of-fit statistics, verify that the graduated curve is both sufficiently smooth and close to the crude data. They support the decision to accept or revise the graduated table.

Question 29Mortality estimation and graduation

Which statement best describes the 'sum of deviations' smoothness test applied to a graduated mortality table?

  1. It compares the graduated rates with the crude rates at a single age only
  2. It examines the pattern of signs of the cumulative deviations between crude and graduated rates Correct answer.
  3. It measures the total number of deaths in the study
  4. It calculates the variance of the exposure population

Explanation

The sum-of-deviations test tracks the cumulative differences between crude and graduated rates and examines how often the sign changes. Frequent sign changes suggest the graduated curve is following random noise rather than a smooth underlying pattern.

Question 30Mortality estimation and graduation

A graduated mortality table is fitted to crude rates by a parametric formula. Which of the following is a parametric graduation method?

  1. Cubic spline smoothing of crude rates
  2. Moving weighted averages of crude rates
  3. Gompertz law of mortality fitted by least squares Correct answer.
  4. Whitaker-Henderson graduation

Explanation

Parametric graduation fits a mathematical formula with a small number of parameters, such as the Gompertz law, to the observed rates. The other listed techniques are non-parametric smoothing methods that do not impose a fixed functional form.

Question 31Mortality estimation and graduation

In the Gompertz law of mortality, the force of mortality is modelled as which function of age?

  1. A reciprocal function of age
  2. A quadratic function of age
  3. An exponential function of age Correct answer.
  4. A linear function of age

Explanation

The Gompertz law specifies that the force of mortality increases exponentially with age, so that the logarithm of the force of mortality is linear in age. This captures the approximately geometric rise in mortality at adult ages.

Question 32Mortality estimation and graduation

Which of the following is a disadvantage of using a parametric graduation such as the Gompertz law?

  1. It always produces rates that are too irregular to be used
  2. It cannot be applied to human mortality data
  3. It may impose a shape on the rates that does not fit the data well at all ages Correct answer.
  4. It requires far more parameters than non-parametric methods

Explanation

Parametric graduation imposes a fixed functional form, so if the true pattern departs from that form, fit may be poor at some ages even though the curve is smooth. This risk of systematic lack of fit is a key drawback.

Question 33Mortality estimation and graduation

The Whitaker-Henderson method of graduation balances which two components?

  1. A term for the number of deaths and a term for population size
  2. A term for exposure and a term for births
  3. A term for net migration and a term for the crude rate
  4. A goodness-of-fit term and a penalty on roughness of the graduated rates Correct answer.

Explanation

Whitaker-Henderson graduation minimises a weighted sum of squared deviations between crude and graduated rates plus a penalty on the roughness of the graduated series. The balance between these terms is controlled by a smoothing constant.

Question 34Mortality estimation and graduation

In Whitaker-Henderson graduation, what is the effect of increasing the smoothing constant?

  1. The graduated curve becomes rougher and fits the crude rates more closely
  2. The graduated curve becomes smoother and fits the crude rates less closely Correct answer.
  3. The graduated curve is unchanged because the constant only affects exposure
  4. The graduated curve becomes smoother and also fits the crude rates more closely

Explanation

The smoothing constant controls the trade-off between fit and smoothness. A larger value places more weight on the roughness penalty, producing a smoother curve that deviates further from the crude data.

Question 35Mortality estimation and graduation

A statistician compares crude and graduated rates and finds that the deviations change sign at almost every age. What does this most likely indicate?

  1. The graduation is over-fitting the random fluctuations in the crude data Correct answer.
  2. The graduation is too smooth and has missed genuine structure
  3. The exposure population was too large
  4. The crude rates were calculated incorrectly

Explanation

Frequent sign changes in the deviations suggest the graduated curve is tracking random noise rather than a smooth underlying pattern, which is a symptom of insufficient smoothing or over-fitting. Increasing the smoothing would reduce the oscillation.

Question 36Mortality estimation and graduation

Which test statistic is commonly used to assess the goodness of fit of graduated rates to crude rates using the number of deaths?

  1. A chi-squared type statistic based on the squared differences between actual and expected deaths Correct answer.
  2. A t-test comparing the mean age at death across two periods
  3. A correlation between age and population size
  4. A coefficient of variation of the exposure population

Explanation

Goodness-of-fit is often assessed with a chi-squared style statistic that sums, over ages, the squared differences between observed deaths and deaths expected under the graduated rates, scaled by the expected variance. Large values indicate poor fit.

Question 37Mortality estimation and graduation

In a mortality investigation, what does the 'exposed to risk' represent?

  1. The number of deaths recorded during the study
  2. The total number of births in the study population
  3. The total time lived by the lives under observation while at risk of dying Correct answer.
  4. The number of people alive at the start of the study

Explanation

Exposure to risk measures the total time each life spends under observation and at risk of the event during the study period. It accounts for entrants, exits and deaths, and forms the denominator of the central death rate.

Question 38Mortality estimation and graduation

Why are crude age-specific mortality rates often unsuitable for direct use in a life table without graduation?

  1. They are only defined for a single age
  2. They may be irregular and non-monotonic because of random variation, especially where exposure is small Correct answer.
  3. They cannot be expressed per thousand lives
  4. They are always too low compared with true mortality

Explanation

Crude rates reflect random fluctuations in deaths and can be erratic, particularly at ages with little exposure, producing an implausible life table. Graduation smooths these irregularities to give a plausible progression across ages.

Question 39Mortality estimation and graduation

In a graduation by reference to a standard table, how are the graduated rates obtained?

  1. By fitting a relationship between the crude rates and the rates of a chosen standard table Correct answer.
  2. By copying the standard table rates directly without adjustment
  3. By replacing the standard table with a parametric formula
  4. By averaging the crude rates with the standard table rates equally

Explanation

Graduation by reference to a standard table models the crude rates as a function of the corresponding standard table rates, then uses the fitted relationship to produce graduated values. This preserves the shape of the standard table while adapting to the data.

Question 40Mortality estimation and graduation

A life table is being constructed from graduated rates for a small insured population with few deaths at older ages. Which practical concern is most relevant when choosing the graduation method?

  1. The method must reproduce every crude rate exactly
  2. The method must use at least ten parameters
  3. The method should ignore exposure entirely
  4. The method should be able to borrow strength from a standard table or parametric form to stabilise sparse rates Correct answer.

Explanation

Where data are sparse, methods that borrow strength, such as parametric graduation or graduation by reference to a standard table, help stabilise the estimates. Exact reproduction of noisy crude rates would defeat the purpose of graduation.

Question 41Mortality estimation and graduation

Which of the following best describes a spline-based graduation approach?

  1. Replacing the crude rates with the standard table rates
  2. Fitting piecewise polynomial curves joined smoothly at knots to the crude rates Correct answer.
  3. Averaging crude rates over fixed age bands
  4. Fitting a single exponential curve over the whole age range

Explanation

Spline graduation fits separate polynomial segments across adjacent age intervals, constrained to join smoothly at the knots. The number and position of knots control the flexibility of the fitted curve.

Question 42Mortality estimation and graduation

In assessing whether a graduated table is acceptable, why is it important that the graduated rates remain close to the crude rates in aggregate, not just point by point?

  1. Aggregate closeness removes the need for smoothness testing
  2. Point-by-point closeness is the only valid measure of fit
  3. Aggregate closeness ensures the total expected deaths are consistent with the observed deaths Correct answer.
  4. Aggregate closeness guarantees the rates are monotonic

Explanation

A graduation that deviates randomly around the crude rates may still fit poorly in aggregate, distorting the total number of expected deaths. Checking aggregate closeness confirms the graduated table reproduces the overall mortality level, not just local patterns.

Question 43Mortality estimation and graduation

Which of the following correctly describes the relationship between the force of mortality and the central death rate when mortality is assumed constant over each year of age?

  1. The central death rate is always exactly twice the force of mortality
  2. The central death rate is independent of the force of mortality
  3. The central death rate equals the force of mortality only at age zero
  4. The central death rate equals the average force of mortality over the year of age Correct answer.

Explanation

When the force of mortality is constant over the year of age, the central death rate equals that constant force, and more generally it approximates the average force over the interval. This link underpins the conversion between rates and forces in graduation.

Question 44Mortality estimation and graduation

A graduated mortality table shows a pronounced hump in mortality around ages 18 to 25. What is the most appropriate interpretation?

  1. This proves the Gompertz law applies at all ages
  2. This indicates the exposure population was too small to measure
  3. This reflects the well-known accident-related mortality hump at young adult ages and may be genuine Correct answer.
  4. This must be an error because mortality should rise monotonically with age

Explanation

Mortality often exhibits a hump at young adult ages driven by accidents and other external causes, so a graduated table showing this feature may be capturing real structure. Graduation should not force monotonicity where the data genuinely deviate.

Question 45Life insurance and annuity contracts

Under a without-profits endowment assurance policy, which benefit is guaranteed to be paid if the life assured survives to the maturity date?

  1. A refund of premiums paid without interest
  2. The sum assured plus declared reversionary bonuses
  3. The sum assured only, with no bonuses added Correct answer.
  4. The asset share accumulated in the insurer's fund

Explanation

A without-profits policy pays a benefit fixed at outset, so survival to maturity triggers payment of the sum assured with no bonuses, since no surplus participation applies. Bonuses and asset-share-linked benefits belong to with-profits or unit-linked contracts, not to this class.

Question 46Life insurance and annuity contracts

A term assurance policy pays the sum assured only if death occurs within the policy term. What is paid if the life assured survives to the end of the term?

  1. The sum assured plus interest
  2. A surrender value equal to premiums paid
  3. The sum assured
  4. Nothing Correct answer.

Explanation

Pure term assurance provides death cover only, so survival to the end of the term produces no benefit payment. The policy simply expires, which is why term assurance is the cheapest form of life cover.

Question 47Life insurance and annuity contracts

In a unit-linked whole life policy, the policyholder's fund is invested in units. Which statement best describes how the death benefit is typically determined?

  1. It is fixed at outset and never varies
  2. It equals the bid value of units plus any guaranteed minimum sum assured Correct answer.
  3. It equals the offer value of units only
  4. It equals the asset share of the insurer's whole with-profits fund

Explanation

Unit-linked death benefits are usually the higher of, or the sum of, the unit fund value and a guaranteed minimum, so the benefit reflects investment performance while retaining a floor. The fund value is normally assessed at bid value for encashment purposes.

Question 48Life insurance and annuity contracts

An annuity certain for a fixed period differs from a whole life annuity in that payments under the annuity certain are made:

  1. Only while the annuitant is alive
  2. For life with a minimum of ten years
  3. For the fixed period regardless of survival Correct answer.
  4. Only if the annuitant survives the period

Explanation

An annuity certain guarantees payments for a defined period whether or not the annuitant survives, so the estate receives any remaining instalments. A whole life annuity, by contrast, ceases on death.

Question 49Life insurance and annuity contracts

A deferred annuity is purchased with a single premium today and begins paying income at age 65. What is the primary purpose of the deferment period?

  1. To accumulate funds so that a higher income can be paid from the chosen retirement age Correct answer.
  2. To reduce the annuity rate by shortening the payment period
  3. To provide death cover during the deferment
  4. To allow the insurer to recover initial expenses before any payout

Explanation

During deferment the premium is invested and accumulates, so the fund at the vesting date supports a larger income than an immediate annuity bought with the same premium. The deferment is a savings phase, not merely an expense-recovery device.

Question 50Life insurance and annuity contracts

Which of the following best describes a reversionary bonus on a with-profits whole life policy?

  1. A bonus paid only if the policy is surrendered early
  2. A one-off bonus paid only on death
  3. An annual addition to the sum assured that, once declared, cannot be removed Correct answer.
  4. A deduction from the sum assured to cover expenses

Explanation

Reversionary bonuses are declared periodically and, once added, become a guaranteed part of the sum assured, so they cannot subsequently be reduced. This guaranteed nature is what distinguishes them from terminal bonuses.