LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – November 2008
ST 5404 – ACTUARIAL STATISTICS
Date : 121108 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PARTA
Answer ALL the questions: (10×2=20 marks)
 Define immediate perpetuity, perpetuity due.
 The amount with compound interest of a certain principal at 5% pa is Rs3969. Find the principal
when the period is 2 years.
 Find the nominal rate p.a convertible halfyearly corresponding to an effective rate of 8% p.a.
 The accumulated value of a certain annuity paid after 8 years at the rate of 8% is 2866.35. Find the
present value.
 Explain deferred annuity due.
 Define L_{x} .
 Explain A_{x} .
 Explain the need for a life table.
 What is the need for a commutation function ?
 Expand S_{x} in terms of D_{x} .
PARTB
Answer FIVE questions: (5×8=40 marks)
 A has taken a loan of Rs2000 at rate of interest 4% pa payable half yearly. He repaid Rs.400 after
2 years,Rs.600 after a further 2 years and cleared all outstanding dues at the end of 7 years from
the commencement of the transaction. What is the final payment made by him?
 Derive the formula for accumulated value and present value of annuity certain due.
 Derive the formula for an increasing annuity .
 Find the present value of an immediate annuity of Rs.600 p.a payable quarterly for 20 years at a
rate of 6% p.a payable half yearly.
 Find the probability that of 2 persons A and B aged 30 and 35 respectively
i.)both die before 55.
ii.)both die after 60.
iii.)A dies before 65 while B dies after 60.
iv.)Atleast one of them survives to 70.
 Obtain the expressions for a_{ x: n} and ( Ia )_{x : n} .
 Calculate the net annual premiums for sum assured of Rs.5000 for the following
assurances on (40)
a.)pure endowment assurance for 20 years.
b.)Temporary assurance for 20 years.
 Obtain the formula for a_{n} and Sn.
PARTC
Answer TWO questions: (2×20=40 marks)
 a) Complete the following life table.
Age l_{x} d_{x} q_{x} L_{x}
10 1000000 – .00409 –
11 – – .00370 –
12 – – .00347 –
13 – – .00342 –
 b) An employee of an institution has to retire at the age of 58.A gratuity benefit of
one months salary for each year of service subject to a maximum benefit of 15
months salary is payable to an employee on retirement or death , as the case may
 Find the probability that:
i.)full gratuity benefit will be payable to a person aged 35, who has just now
completed 5 years of service.
ii.)the gratuity benefit will not exceed 10 months salary .
iii.)the gratuity benefit will be atleast 12 months salary.
iv.)the employee earns atleast 12months salary as gratuity benefit payable at
death.
 a) A loan of Rs.5000 is to be repaid with interest at 8% p.a be means of an
immediate annuity for 10 years. Find the yearly installment. What will be the
principal and interest contained in the 5th installment? What will be the principal
outstanding immediately after the 8th payment is made?
 b) Find the present value of an immediate annuity of Rs.240 p.a payable in equal
monthly installments for 10 years certain at nominal interest of 8% p.a convertible
half yearly.
 a) A person aged 30 years approached a life office for special type of policy providing for the
following benefits.
i.)Rs.1000 on death during the first 5 years.
ii.)Rs.2000 on death during the next 15 years.
iii.)survival benefit of Rs.500 at the end of the 5th year .
iv.)Further payment of Rs.2000 on survival of 20 years.
Find the annual premium assuming that the premium paying term is 20 years.
 b) Derive the expression for A_{x: n} and (IA )_{x: n} .
 a) A had decided to invest Rs.500 at the end of each year. He did so far 7 years.
Then there was a gap of 4 years. He could again invest Rs.500 p.a for the next 4
years beginning from the end of the 12th year. Find the amount to his credit at the
end of the 15th year assuming interest rate of 9% p.a.
 b) A payment of Rs.P falls due at the end of every γ years .Find at the rate of
interest of i p.a the present value of the payments to be paid during n years ( n is
an exact multiple of γ).