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IAI CP1 practice questions

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Question 1Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Under the equivalence principle, the net single premium for a life insurance contract is set so that which quantity equals zero at issue?

  1. The gross premium loading percentage
  2. The variance of the insurer's claim payments
  3. The policyholder's surrender value
  4. The expected present value of the insurer's profit Correct answer.

Explanation

The equivalence principle equates the expected present value of premiums with that of benefits, so the expected present value of profit (the insurer's loss random variable) is set to zero at issue. This is a fundamental pricing principle in life contingencies.

Question 2Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

A whole life annuity-due of 1 per year is payable annually to a life aged x. Which expression gives its actuarial present value?

  1. a-double-dot-x = sum over k of v^k times kqx
  2. a-double-dot-x = A-x divided by d
  3. a-double-dot-x = (1 - A-x) divided by i
  4. a-double-dot-x = sum over k of v^k times kpx Correct answer.

Explanation

An annuity-due pays at the start of each year, so the present value is the sum over k from 0 of v^k multiplied by the probability of survival to k. Equivalently, a-double-dot-x = (1 - A-x)/d, using the discount rate d, not i.

Question 3Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

For a life table with radix l-0, the one-year death probability q-x is best expressed as which ratio?

  1. (l-x minus l-x+1) divided by l-x Correct answer.
  2. l-x divided by l-x+1
  3. l-x+1 divided by l-x
  4. (l-x minus l-x+1) divided by l-x+1

Explanation

q-x is the probability a life aged x dies before age x+1, computed as deaths in the year divided by survivors at the start. That is (l-x - l-x+1)/l-x.

Question 4Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which statement best describes the role of a reserve (net premium reserve) in life insurance?

  1. It is the expected present value of future benefits minus future net premiums at a given duration Correct answer.
  2. It is the maximum benefit the insurer will ever pay
  3. It is the loading added to cover commission costs
  4. It is the accumulated value of all premiums paid to date

Explanation

The net premium reserve at duration t is the prospective excess of the present value of future benefits over future net premiums. It represents funds held to meet obligations on in-force policies.

Question 5Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

In a multiple decrement model, the independent (associated single decrement) rate q-x-prime for cause j is related to the dependent rate by which assumption?

  1. Uniform distribution of each decrement over the year of age Correct answer.
  2. Independence of the interest rate
  3. Constant force of mortality only for the total
  4. No mortality at all in the model

Explanation

Converting dependent multiple decrement rates to independent rates typically assumes a uniform distribution of each decrement (or constant force) across the year. This lets actuaries back out the associated single decrement rates.

Question 6Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An insurer prices a term assurance using a gross premium that includes a fixed expense e at the start of each year. Under the equivalence principle, the gross premium G satisfies which condition?

  1. Gross premium equals net premium exactly
  2. Expected present value of premiums equals expected present value of benefits plus expenses Correct answer.
  3. Expected present value of benefits equals the variance of expenses
  4. Expected present value of expenses equals zero

Explanation

With expenses, the equivalence principle equates the expected present value of gross premiums to the sum of expected present value of benefits and expenses. This yields the gross premium.

Question 7Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

If the force of interest is constant at delta, the present value of 1 payable in t years equals which expression?

  1. 1 plus delta times t
  2. e to the power minus delta times t Correct answer.
  3. e to the power delta times t
  4. 1 divided by (1 plus delta) to the power t

Explanation

Under a constant force of interest, discounting uses the exponential function: v^t = e^(-delta t). This is the standard continuous discounting formula.

Question 8Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

For a life aged x, the expected present value of a whole life assurance paying 1 at the end of the year of death is denoted A-x. Which identity links A-x and the annuity-double-dot a-x?

  1. A-x = d times a-double-dot-x
  2. A-x = 1 plus i times a-double-dot-x
  3. A-x = 1 minus i times a-double-dot-x
  4. A-x = 1 minus d times a-double-dot-x Correct answer.

Explanation

The standard identity is A-x = 1 - d*a-double-dot-x, where d is the discount rate. This follows from the annuity relationship a-double-dot-x = (1 - A-x)/d.

Question 9Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which of the following best explains why a select mortality table shows lower mortality in the first few policy years than an aggregate table?

  1. Premiums are lower in early policy years
  2. Interest rates are higher in early policy years
  3. Underwriting selects healthier lives, and the effect wears off over time Correct answer.
  4. Reserves are lower in early policy years

Explanation

Select mortality reflects the temporary effect of underwriting at entry: selected lives experience lighter mortality initially, converging toward ultimate rates over time. This is why select and ultimate tables differ in early durations.

Question 10Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

A portfolio has independent lives each with mortality q. For a group of n independent lives, the number of deaths D is modelled as which distribution?

  1. Binomial with parameters n and q Correct answer.
  2. Poisson with mean q
  3. Normal with mean n and variance q
  4. Exponential with rate n

Explanation

With n independent lives each having the same death probability q, the death count is Binomial(n, q). This underpins risk pooling and the calculation of mortality fluctuations.

Question 11Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

In the context of pension funding, which method determines contributions so that the present value of future benefits equals the present value of future contributions plus existing assets?

  1. The projected unit credit method applied prospectively Correct answer.
  2. The terminal funding method
  3. The aggregate cost method using only past service
  4. The pay-as-you-go method

Explanation

Prospective funding methods such as projected unit credit set contributions so that future benefits are matched by future contributions plus current assets. This is the actuarial funding principle behind many pension schemes.

Question 12Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which statement about the variance of the present value of a life insurance liability is correct?

  1. It is unaffected by the size of the sum assured
  2. It increases with the variability of the underlying mortality and interest assumptions Correct answer.
  3. It equals the expected present value of benefits
  4. It is always zero under the equivalence principle

Explanation

The variance of the present value reflects uncertainty in mortality and interest experience, so it rises with the variability of those assumptions. The equivalence principle controls the mean, not the variance.

Question 13Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

For a deferred annuity-due of 1 per year payable from age x+n to a life now aged x, the actuarial present value is best written as which expression?

  1. nEx divided by a-double-dot-x+n
  2. a-double-dot-x minus a-double-dot-x+n
  3. n-year deferred annuity-due = nEx times a-double-dot-x+n Correct answer.
  4. nEx plus a-double-dot-x+n

Explanation

A deferred annuity-due equals the probability-and-interest discounted value of surviving to the deferment period, nEx, multiplied by the annuity-due value at the deferred age. This is the standard deferment relationship.

Question 14Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which of the following is the most appropriate description of a unit-linked (unitised) life insurance contract?

  1. Benefits are fixed at issue and never vary
  2. Benefits are paid only on survival to maturity
  3. Benefits depend only on the insurer's mortality experience
  4. Benefits are linked to the value of an underlying investment fund, with mortality and expense charges deducted Correct answer.

Explanation

Unit-linked contracts tie the policy value to units in an investment fund, while the insurer deducts mortality and expense charges. Investment risk is largely borne by the policyholder.

Question 15Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

If the effective annual interest rate is i, the present value of 1 due at the end of year 3 is which expression?

  1. (1 plus i) cubed
  2. (1 plus i) to the power minus 3 Correct answer.
  3. 3 divided by (1 plus i)
  4. 1 plus 3i

Explanation

Discounting a payment at the end of year 3 uses v^3 = (1+i)^(-3). This is the standard compound discounting formula.

Question 16Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

In a competing-risk (multiple decrement) model, the probability of decrement from cause j during the year, given survival to age x, is obtained by which operation?

  1. Dividing the total force of decrement by j
  2. Integrating the cause-specific force of decrement over the year, adjusted for all other decrements Correct answer.
  3. Adding the forces of all causes together
  4. Multiplying the independent rates of all causes

Explanation

The dependent probability for cause j is the integral of the cause-specific force multiplied by the overall survival probability over the year. This accounts for the presence of the other competing decrements.

Question 17Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which assumption allows the actuary to express the total force of decrement as the sum of the cause-specific forces in a multiple decrement model?

  1. Each cause acts independently on the individual Correct answer.
  2. The interest rate is zero
  3. Decrements occur only at year-end
  4. All causes have identical forces

Explanation

When each decrement cause operates independently, the total force of decrement is the sum of the cause-specific forces. This additivity is the foundation of the multiple decrement framework.

Question 18Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary uses the recurrence relation for reserves: V-t plus P equals q times (S minus V-t+1) plus V-t+1, discounted. This relation is best described as which approach?

  1. A prospective formula ignoring mortality
  2. A method that assumes zero interest
  3. A retrospective recursion linking successive reserves Correct answer.
  4. A formula for gross premium only

Explanation

The reserve recursion expresses the reserve at duration t plus the premium as the discounted expected cost of claims plus the next reserve. It is a retrospective/prospective recursion used to roll reserves forward.

Question 19Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

In profit testing, the profit signature of a policy is best described as which of the following?

  1. The reserve held at each duration
  2. The sequence of expected profits by policy year, allowing for the cost of capital Correct answer.
  3. The total premium collected over the policy term
  4. The sum assured payable on death

Explanation

The profit signature is the stream of expected annual profits emerging over the policy's life, often discounted or adjusted for the cost of capital. It is central to profit testing and product design.

Question 20Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which statement correctly distinguishes a with-profit from a non-profit life insurance contract?

  1. Non-profit policies share in investment surpluses
  2. Non-profit policies always pay higher benefits than with-profit policies
  3. With-profit policies may receive bonuses based on the insurer's experience, while non-profit policies have fixed benefits Correct answer.
  4. With-profit policies cannot pay death benefits

Explanation

With-profit contracts allow policyholders to share in surplus through bonuses, whereas non-profit contracts specify fixed benefits. This distinction affects pricing and reserving.

Question 21Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

For a life annuity payable continuously at rate 1 per year, the actuarial present value a-bar-x is expressed as which integral?

  1. The sum over k of v^k times kpx
  2. The integral from 0 to infinity of tpx dt
  3. The integral from 0 to infinity of v^t times tpx dt Correct answer.
  4. The integral from 0 to infinity of v^t times tqx dt

Explanation

A continuous annuity pays at rate 1 while the life survives, so its present value is the integral of v^t times the survival probability tpx over all t. This is the continuous analogue of the annuity-due sum.

Question 22Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which of the following best describes the purpose of a surrender value in a life insurance policy?

  1. It is the amount payable if the policyholder terminates the policy before maturity Correct answer.
  2. It is the maximum death benefit payable
  3. It is the premium paid in the first year
  4. It is the reserve held for expenses

Explanation

A surrender value is the cash amount paid to the policyholder on early termination of the policy. It is typically related to, but less than, the reserve.

Question 23Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

A life aged 40 purchases a 20-year endowment assurance with sum assured 100,000. Which statement about the benefit is correct?

  1. It pays 100,000 at age 40 immediately
  2. It pays 100,000 on death within 20 years or on survival to age 60, whichever occurs first Correct answer.
  3. It pays only if the life survives to age 60
  4. It pays only if the life dies within 20 years

Explanation

An endowment assurance combines term assurance and a pure endowment: the sum assured is paid on death during the term or on survival to the end of the term, whichever happens first.

Question 24Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which of the following is the correct interpretation of a survival probability of 5p-40 equal to 0.98?

  1. The probability a life aged 40 dies before 45 is 0.98
  2. The probability a life aged 45 survives 5 years is 0.98
  3. The probability a life aged 40 survives to age 45 is 0.98 Correct answer.
  4. The expected number of deaths between 40 and 45 is 0.98

Explanation

Notation such as 5p-40 denotes the probability that a life aged 40 survives five years to age 45. The value 0.98 means survival is very likely over that period.

Question 25Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

Which of the following best explains why actuaries use a risk discount rate in profit testing?

  1. It is the mortality rate used in the model
  2. It reflects the return required by the insurer's capital providers and discounts emerging profits Correct answer.
  3. It is the rate used to accumulate reserves
  4. It equals the guaranteed interest rate on the policy

Explanation

The risk discount rate represents the return required on capital and is used to discount the emerging profit stream to a present value. It captures the cost of capital and risk in product pricing.

Question 26Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating an annuity factor using the standard actuarial approximation for a life annuity-due, ä_x ≈ ä_x - 0.5. Which refinement of this approximation accounts for the fact that deaths are not uniformly distributed across each year of age?

  1. Subtracting the full force of mortality from the annuity factor
  2. Adding a correction term based on the expected fraction of a year lived by those dying in the year of death Correct answer.
  3. Replacing the annuity-due with an annuity-immediate and adding one full payment
  4. Multiplying the annuity factor by the one-year survival probability

Explanation

The standard 0.5 correction assumes deaths occur on average halfway through the year. When mortality is concentrated early or late in the year, the average fraction of a year lived by decedents differs from 0.5, so a correction based on that fraction refines the approximation. This is the basis of refinements such as the Woolf or similar adjustments.

Question 27Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

A life aged exactly 60 is subject to a constant force of mortality μ = 0.02 per year. Using the exponential survival model, what is the probability that this life survives to age 65, expressed to three decimal places?

  1. 0.980
  2. 0.905 Correct answer.
  3. 0.819
  4. 0.951

Explanation

Under a constant force of mortality, the survival probability over t years is exp(-μt). Here t = 5 and μ = 0.02, so the probability is exp(-0.10) = 0.9048, which rounds to 0.905.

Question 28Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An insurer is modelling the number of deaths among a group of independent lives where each life has the same one-year death probability q. Which distribution best describes the total number of deaths in the group?

  1. Binomial distribution with parameters n and q Correct answer.
  2. Geometric distribution with parameter q
  3. Normal distribution with mean nq and variance nq(1-q) exactly
  4. Poisson distribution with mean nq exactly

Explanation

With n independent lives each having identical death probability q, the number of deaths is a sum of n independent Bernoulli trials, which is Binomial(n, q). The Poisson and Normal are approximations valid under particular limiting conditions, not exact descriptions. The Geometric distribution models the number of trials until the first death, not the total count.

Question 29Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is computing the expected present value of a whole life assurance paying the sum assured at the moment of death, rather than at the end of the year of death. How does this continuous benefit compare with the annual-benefit version, all else equal?

  1. The continuous benefit has a higher expected present value because payment occurs earlier on average Correct answer.
  2. The continuous benefit has a lower expected present value because the sum assured is discounted for longer
  3. The two have identical expected present values under any mortality law
  4. The continuous benefit is higher only when the interest rate is zero

Explanation

Paying at the moment of death means, on average, payment is made earlier than at the end of the year of death. Earlier payment means less discounting, so the expected present value is higher (assuming positive interest). The relationship is captured by the factor relating A-bar and A.

Question 30Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

A pension scheme uses the projected unit credit method. Which statement best describes how the normal contribution is determined under this method?

  1. It covers the present value of benefits accruing in the current year plus an adjustment for past service deficits Correct answer.
  2. It equals the total present value of all future benefits divided by the remaining working lifetime
  3. It is the difference between the scheme's assets and liabilities at the valuation date
  4. It is set equal to the interest earned on the scheme assets each year

Explanation

Under projected unit credit, the normal contribution relates to the benefits earned in the current period, with separate amortisation of any surplus or deficit from past service. This contrasts with methods that spread the total cost evenly across service. The past service element is treated as a separate supplementary contribution.

Question 31Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the net premium for a 10-year term assurance on a life aged 45. Which principle determines the net premium in the equivalence principle?

  1. The premium is chosen so the reserve is zero at the end of each year
  2. The premium is set so the probability of loss is at most five per cent
  3. The premium equals the sum assured divided by the policy term
  4. The expected present value of premiums equals the expected present value of benefits Correct answer.

Explanation

The equivalence principle sets the net premium so that the expected present value of premiums equals the expected present value of benefits, ignoring expenses and profit. This is a first-moment condition; other principles (such as percentile or exponential utility) are alternatives. Reserves being zero throughout would imply no prefunding of benefits.

Question 32Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the retrospective reserve for a policy at duration t. Which quantity does the retrospective reserve represent?

  1. The present value of all future benefits less the present value of future premiums
  2. The total premiums paid to date without interest
  3. The difference between the sum assured and the reserve at the prior duration
  4. The accumulated value of past premiums less the accumulated value of past benefits and expenses, allowing for survivorship Correct answer.

Explanation

The retrospective reserve is the accumulated fund built from past premiums after deducting past benefits and expenses, accumulated with interest and adjusted for survivorship. In a consistent basis it equals the prospective reserve. The prospective reserve is the present value of future benefits less future premiums.

Question 33Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is testing the sensitivity of a whole life assurance premium to the valuation basis. If the valuation interest rate is increased while mortality is held constant, what happens to the net premium?

  1. The net premium decreases because benefits are discounted more heavily Correct answer.
  2. The net premium increases because mortality is unaffected
  3. The net premium is unchanged because interest does not affect premiums
  4. The net premium increases because the insurer earns less on reserves

Explanation

A higher valuation interest rate reduces the present value of both benefits and premiums, but the effect on benefits dominates for a whole life assurance, so the net premium falls. Interest affects the timing-weighted value of benefit payments more strongly than level premium payments.

Question 34Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is computing the variance of the present value of a life assurance benefit. Which feature of the benefit distribution is most important in determining this variance?

  1. The number of policyholders in the portfolio only
  2. The mean of the sum assured only
  3. The rate of expense inflation only
  4. The variability of the timing of the death benefit payment Correct answer.

Explanation

The variance of the present value of a single life assurance arises mainly from uncertainty in the time of death, which drives the discounting and hence the present value. For a portfolio of independent lives, diversification reduces the variance relative to the mean. The mean sum assured alone does not capture dispersion.

Question 35Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary models two independent lives aged 50 and 55 under a joint-life first-death assurance. Which statement correctly describes when the benefit is paid?

  1. The benefit is paid on the death of the younger life only
  2. The benefit is paid only when both lives have died
  3. The benefit is paid on the death of the older life only
  4. The benefit is paid on the first death of either life Correct answer.

Explanation

A joint-life first-death assurance pays the sum assured on the first death among the lives covered, ending the contract. The survival of the joint-life status requires all lives to survive, so the benefit is triggered by the earliest death.

Question 36Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is valuing a deferred temporary annuity-due payable to a life aged 50, deferred for 10 years and payable for 5 years thereafter. Which expression gives the actuarial present value using standard commutation functions?

  1. (D_60 - D_65) / D_50
  2. (N_50 - N_60) / D_50
  3. (M_60 - M_65) / D_50
  4. (N_60 - N_65) / D_50 Correct answer.

Explanation

A deferred temporary annuity-due payable from age 60 to 65 is valued using the ratio of the difference of annuity-due commutation functions to the discount function at age 50. The expression (N_60 - N_65)/D_50 correctly captures the deferred temporary annuity-due. The M functions relate to assurance, not annuities.

Question 37Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating a select mortality rate for a policy in its third year. Which feature distinguishes select mortality from aggregate mortality in the early policy years?

  1. Select mortality applies only to pension scheme members
  2. Select mortality is higher in the first few years because of adverse selection
  3. Select mortality is identical to aggregate mortality in all policy years
  4. Select mortality is lower in the first few years because of underwriting selection Correct answer.

Explanation

Underwriting at entry screens out high-risk lives, so mortality in the first few policy years is lower than the ultimate level. Select mortality tables capture this effect with duration-dependent rates that grade into ultimate rates. Aggregate tables blend all durations and so do not reflect this selection effect.

Question 38Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the expected present value of a term assurance using the relation between assurance and annuity functions. Which identity correctly links the whole life assurance A_x and the annuity-due ä_x under a constant effective interest rate i?

  1. A_x = d·ä_x
  2. A_x = 1 + d·ä_x
  3. A_x = v·ä_x
  4. A_x = 1 - d·ä_x, where d = i/(1+i) Correct answer.

Explanation

The identity A_x = 1 - d·ä_x follows from the relationship between the present value of a whole life assurance and a whole life annuity-due, where d is the discount rate. It reflects the fact that a payment of 1 now can be split into interest and survival components. The other forms do not satisfy the standard identity.

Question 39Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is assessing the impact of a change in the risk discount rate on the profit signature of a policy. If the risk discount rate is increased, what happens to the present value of the profit signature?

  1. The present value increases because the insurer requires a higher return
  2. The present value is unchanged because profits are fixed
  3. The present value decreases because future profits are discounted more heavily Correct answer.
  4. The present value increases because the profit signature is unaffected

Explanation

The present value of the profit signature is the sum of discounted future profits using the risk discount rate. Raising the discount rate reduces the present value of each future profit, so the total present value falls. The profit signature itself (the sequence of profits) is unchanged; only its valuation changes.

Question 40Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is explaining the operation of a unit-linked contract to a client. Which statement correctly describes how the policyholder's fund is treated?

  1. The fund is invested in units whose value fluctuates with the underlying assets, and the policyholder bears the investment risk Correct answer.
  2. The fund is held in the insurer's non-profit fund and smoothed over time
  3. The fund is credited with a fixed rate of interest guaranteed by the insurer
  4. The fund is invested in units but the insurer guarantees the unit price

Explanation

In a unit-linked contract, premiums are used to buy units in an underlying fund, and the value of the policy fluctuates with the unit price. The policyholder typically bears the investment risk, in contrast with non-profit or with-profit contracts where the insurer bears or shares the risk.

Question 41Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating a one-year survival probability from a life table. If q_40 = 0.004, what is p_40?

  1. 0.998
  2. 0.999
  3. 0.996 Correct answer.
  4. 0.004

Explanation

The one-year survival probability is p_40 = 1 - q_40 = 1 - 0.004 = 0.996. This follows directly from the complement rule for the two mutually exclusive outcomes of survival and death within the year.

Question 42Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is valuing a with-profit policy where the insurer declares reversionary bonuses. Which statement correctly describes a reversionary bonus?

  1. It is added to the sum assured and becomes payable on death or maturity, and may itself attract future bonuses Correct answer.
  2. It is a bonus paid in cash each year and not added to the sum assured
  3. It is a reduction in premium granted at the policy anniversary
  4. It is a one-off terminal payment made only at maturity

Explanation

A reversionary bonus is declared periodically and added to the sum assured, becoming payable when the claim arises. Simple reversionary bonuses do not themselves earn further bonuses, while compound reversionary bonuses do. A terminal bonus is a separate, one-off addition paid at maturity or death.

Question 43Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the expected present value of a pure endowment payable to a life aged 30 if the life survives to age 60. Which expression is correct using standard notation?

  1. v^30 · 30q_30
  2. v^30 · 30p_30 Correct answer.
  3. 30p_30
  4. v^30

Explanation

A pure endowment pays the sum assured only if the life survives the term, so the expected present value is the discounted survival probability. With a term of 30 years, this is v^30 times the probability of survival, 30p_30. The death probability or the discount factor alone would not capture both elements.

Question 44Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is explaining the concept of a surrender value to a policyholder who wishes to terminate a whole life policy early. Which statement correctly describes the surrender value?

  1. It is the amount payable on early termination, typically reflecting the accumulated reserve less a surrender charge Correct answer.
  2. It is the present value of future premiums the policyholder would have paid
  3. It is the total premiums paid to date with no deductions
  4. It is the full sum assured payable on death

Explanation

On early termination, the policyholder may receive a surrender value, which generally reflects the accumulated reserve adjusted for expenses and a surrender charge. It is not the full sum assured, which is payable only on death, and it typically reflects the insurer's costs of early termination.

Question 45Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the probability that a life aged 45 dies between ages 50 and 55. Which expression gives this probability in terms of survival probabilities?

  1. 5q_45 - 10q_45
  2. 5p_45 - 10p_45 Correct answer.
  3. 10p_45 - 5p_45
  4. 5p_45 + 10p_45

Explanation

The probability of surviving to age 50 but dying before age 55 is the probability of surviving 5 years minus the probability of surviving 10 years, i.e. 5p_45 - 10p_45. This difference captures the lives still alive at 50 who do not reach 55.

Question 46Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is valuing a benefit that is paid at the end of the year of death, but only if death occurs after a deferred period of n years. Which statement correctly describes the expected present value of this deferred assurance?

  1. It equals the whole life assurance value plus the value of a term assurance covering the deferment period
  2. It equals the value of a term assurance covering the deferment period
  3. It equals the whole life assurance value minus the value of a term assurance covering the deferment period Correct answer.
  4. It equals the value of a pure endowment for the deferment period

Explanation

A deferred whole life assurance pays only if death occurs after the deferment period. Its value equals the whole life assurance value less the value of a term assurance covering the deferment period, since the term assurance covers the deaths that would otherwise be paid in that period.

Question 47Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the expense loading for a whole life policy. Which statement correctly describes the purpose of the expense loading in a gross premium?

  1. It is an amount added to the reserve at each year end
  2. It provides for the present value of future expenses so that the gross premium covers both benefits and expenses Correct answer.
  3. It is a deduction from the sum assured at maturity
  4. It is a tax levied on the policyholder by the regulator

Explanation

The gross premium includes an expense loading to cover the present value of expected future expenses, in addition to the net premium for benefits. This ensures the premium is sufficient to meet both benefit and expense outgo. The loading is not a reserve addition or a regulatory tax.

Question 48Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is assessing the effect of mortality improvement on the value of a life annuity. If mortality improves so that lives live longer, what happens to the actuarial present value of a whole life annuity-due?

  1. It decreases because the annuity factor is smaller
  2. It increases because expected payments are made over a longer period Correct answer.
  3. It is unchanged because the interest rate is fixed
  4. It decreases because the survival probability is lower

Explanation

Improved mortality means lives survive longer on average, so more annuity payments are expected. This increases the actuarial present value of the annuity. The effect is the opposite for a whole life assurance, whose value tends to fall as mortality improves.

Question 49Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is calculating the probability that both of two independent lives aged 60 and 65 survive for 5 years. If 5p_60 = 0.90 and 5p_65 = 0.80, what is the joint survival probability?

  1. 0.10
  2. 0.85
  3. 0.72 Correct answer.
  4. 0.17

Explanation

For independent lives, the joint survival probability is the product of the individual survival probabilities. Here 0.90 × 0.80 = 0.72. Independence is the key assumption; without it the calculation would require a joint distribution.

Question 50Actuarial practice / core technical application (domain names and weights not enumerated in the official source)

An actuary is explaining the role of a terminal bonus in a with-profit contract. Which statement correctly describes the purpose of a terminal bonus?

  1. It rewards persistency and reflects investment gains not yet distributed through regular bonuses Correct answer.
  2. It is a fixed amount stated in the policy schedule at outset
  3. It is paid only on surrender and not on maturity
  4. It replaces the regular reversionary bonus entirely

Explanation

A terminal bonus is a discretionary addition paid at maturity or death, reflecting the policyholder's share of investment gains not already distributed through regular reversionary bonuses. It also helps discourage early surrender. It does not replace regular bonuses and is not fixed at outset.