Will you please share the previous year question paper of Institute of Actuaries Of IndiaSubject CT5 General Insurance, Life and Health Contingencies Exam???
Here I am sharing the previous year question paper of Institute of Actuaries Of IndiaSubject CT5 General Insurance, Life and Health Contingencies Exam
Q. 1) State whether the following equations are correct or not, and, where applicable, suggest
correction.

: = : :
[2]
Q. 2) i) Calculate the value of 1.75p45.5 on the basis of mortality table AM92 Ultimate and
assuming that deaths are uniformly distributed between integral ages.
(3)
ii) Explain how occupation affects morbidity and mortality. Your explanation should also be
supported by examples.
(3)
[6]
Q. 3) i) A temporary life annuity is payable continuously to a life exactly aged 60 for a 10 year
term. The rate of payment during the first 5 years is Rs. 50,000 per annum and thereafter it
is Rs.60,000 per annum. The force of mortality for this life is 0.03 between the ages of 60
and 65, and 0.04 between the ages of 65 and 70.
Calculate the expected present value of this annuity assuming a force of interest of 5% per
annum.
(5)
ii) Assuming that mortality and interest rates are as in (i) above, calculate the expected
present value of:
(a) A 10year term assurance issued to the life in (i) for a sum assured of Rs. 2,50,000
payable immediately on death
(b) A 10year endowment assurance issued to the life in (i), which pays Rs. 2,50,000 on
maturity or immediately on earlier death.
(4)
[9]
Q. 4) Let X be a random variable representing the present value of the benefits of a pure
endowment contract and Y be a random variable representing the present value of the benefits
of a term assurance contract which pays the death benefit at the end of the year of death. Both
contracts have unit sum assured, a term of n years and were issued to the same life aged x.
(i) Derive and simplify as far as possible using standard actuarial notation an expression for
the covariance of X and Y.
(3)
(ii) Hence or otherwise, derive an expression for the variance of (X+Y) and simplify it as far
as possible using standard actuarial notation.
(4)
[7]
σx
ρx µx νx
Q. 5) A population is subject to two modes of decrements, α and β, between ages x and x + 1. In the
single decrement tables p α x x t and p β x x t
where 0 ≤ t ≤ 1.
Write down an integral expression for (aq)x
α and hence obtain an expression for this
probability in terms of x only.
[5]
Q. 6) Twins exactly aged 30 years purchase a special annuity policy providing a fully continuous
joint life annuity along with a provision for joint life insurance. Their future lifetimes are
independent and identically distributed. The policy pays the following benefits:
• Rs. 100,000 per year while both are alive
• Rs. 100,000 at the time of the first death
• Rs. 60,000 per year after the first death until the second death
• Rs. 80,000 at the time of the second death
The constant force of interest (δ) is 5% per annum and the constant force of mortality
µx(t) = 0.04 for all x and t.
(a) Show that:
a
(2)
(b) Calculate the actuarial present value of this special annuity (with insurance provision). (6)
[8]
Q. 7) An insurer sells a product providing the life insurance and sickness benefit of term 20 years to
healthy lives aged 35. The policies pay a lump sum of Rs. 200,000 immediately on death,
with an additional Rs. 100,000 if the deceased is sick at the time of death. There is also a
benefit of Rs. 30,000 per annum payable continuously to sick policyholders. There is no
waiting period before benefits are payable. Annual premiums of Rs. 5,000 are payable
continuously by healthy policyholders.
The mortality and sickness of the policyholders are described by the following multiple state
model, in which the forces of transition µ, ν, ρ and σ depend on age.
H: Healthy S: Sick
D: Dead
pgh
x,t is the probability that a life aged x in state g (g = H, S, D) will be in state h at age
x + t (t ≥ 0 and h = H, S, D). The force of interest is δ.
Express in integral form, using the probabilities and the various forces of transition, the
expected present value of a policy at its commencement.
[4]
Q. 8) A life insurance company has been selling 3 year unit linked policies to lives aged exactly
30 years. The charges under the policies are as under:
Allocation Charge: First Year 20%, other years 2%
Policy charge: Rs. 600 at start of first year and subsequently inflating at 5%
per annum
Mortality Charge: 110% * Standard Table mortality rate * max (Sum Assured –
Unit Fund, 0)
Fund Management Charge: 1.25% per annum
All charges, except Fund Management Charge (FMC), are deducted at start of the year. The
mortality charge is calculated after deducting the policy charge from the unit fund at start.
FMC is deducted at end of year.
The other details are as follows:
Annual premium: Rs. 10,000
Sum Assured (SA): Rs. 100,000
Unit growth rate: 8% per annum
Standard Table mortality rates:
Age 30 31 32
Mortality Rate 0.001 0.002 0.003
The company is planning to offer an additional guaranteed benefit equal to 5% of the annual
premium payable on maturity. To be able to meet this guarantee cost, it intends to have an
additional charge expressed as percentage of unit fund. This guarantee charge would be
deducted at start of each year after deducting the policy charge and mortality charge from the
unit fund at start. The guarantee charge would be invested such that it earns 6% per annum.
(Ignore premium lapses and surrenders).
(a) By projecting the unit fund for all 3 years, show that a guarantee charge of 0.9% per
annum would be sufficient to meet the guarantee cost.
Each year, the company allocates units to the policyholder based on the allocated premium
and the unit price at start of year. Unit price is defined as:
(8)
Unit price (t) = Unit Fund (t) / Number of Units (t), at time t
Only policy charge, mortality charge and guarantee charge is deducted by cancellation of
units based on the unit price at start of year. Unit price at start of year 1 is 10.
(b) Based on the results in part (a), determine the number of units and the unit price at end of
each year.
(5)
[13]
Q. 9) A life insurance company issued fiveyear term assurance policies exactly two years ago to
lives all aged exactly 34 years then, for a regular premium of Rs. 500 and a sum assured of
Rs. 125,000. The number of policies remaining is 25 and reserve per policy is Rs. 231, as on
date. The expected future profit for the remaining three years from this block of policies is
(?, 1800, 1700).
The company has total assets of Rs. 25,000 as on date.
The company expects to sell 10 policies of fouryear without profit endowment assurance to
policyholders all aged exactly 35 years for a single premium of Rs. 50,000 and a sum assured
of Rs. 62,500 payable on maturity or at the end of the year of death if earlier. On surrender,
the policyholder would receive single premium paid less surrender penalty.
The company uses the following best estimate assumptions for endowment assurance for
profit testing:
Year Mortality
Rate
Surrender rate Surrender Penalty
(as % of single
premium)
Expenses at start
year per policy
1 0.0015 5.0% 10.0% 1000
2 0.0020 2.5% 5.0% 200
3 0.0025 1.5% 2.5% 210
4 0.0030 0.0% 0.0% 220
Mortality rate and expense for future years for term assurance are the same as in the above
table starting from Year 2. Lapse rate assumption for the third policy year is zero and for
future years it is not provided.
Deaths and surrenders occur at the end of the year. The surrender rates are applied to the
number of policies in force at each year end i.e. on policies remaining after deaths.
Reserves at the end of each year are equal to the present value of all future benefits and
expenses less present value of future premiums. Surrenders are ignored while calculating the
reserves. The mortality assumption and expense assumption are 15% higher than the best
estimate assumption for reserving purpose. Valuation interest rate is 5% per annum.
(a) Calculate the reserves per policy at end of each year for endowment assurance.
Net Assets is defined as total assets less total reserves. Net Assets increase or decrease by the
amount of profit/loss in a given year.
(3)
(b) If the embedded value is equal to the Net Assets plus the net present value, determine the
embedded value at end of next year. Use an investment rate of 6.5% per annum and a risk
discount rate of 13% per annum.
(14)
(c) Without doing any further calculations, explain the impact of a decrease in the valuation
interest rate on the embedded value.
(2)
[19]
Q. 10) (a) Two life insurance companies in the same country maintain records of inforce policies and
deaths subdivided by age and policy duration. Outline the advantages and disadvantages
of pooling the data of the two companies to form one mortality rate estimate for each
combination of age and policy duration.
(3)
(b) Mortality levels for a certain country have been studied at national and regional level.
Under what circumstances a particular region may have an Area Comparability
Factor of 0.5.
(1)
[4]
Q. 11) On 1 January 1996 a life office issued a number of 20year pure endowment policies to a
group of lives aged 40 exact. In each case, the sum assured was Rs. 75,000 and premiums
were payable annually in advance.
On 1 January 2010, 500 policies were still in force. During 2010, 3 policyholders died, and no
policy lapsed for any other reason.
The office calculates net premiums and net premium reserves on the following basis:
Interest: 4% per annum
Mortality: AM92 Select
(i) Calculate the profit or loss from mortality for this group for the year ending
31 December 2010.
(7)
(ii) Explain why the mortality profit or loss has arisen.
(2)
[9]
Q. 12) The premiums payable under a deferred annuity contract issued to women aged exactly 60 are
limited to 5 years. The annuity commences at age 65, provided the policyholder is still alive
at that age. The annuity provides payments of Rs. 35000 payable annually in advance for 5
years certain (i.e. it continues to be paid for 5 years even if the annuitant dies before age 69)
and for life thereafter. There is no benefit if the policyholder dies before age 65.
(i) Calculate the annual premium. (6)
(ii) Calculate the retrospective and prospective reserves after the policy has been in force for
each of 5 and 10 years.
Basis: PFA92C20 mortality, 4% pa interest
(8)
[14]
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