Loyola College B.Sc. Statistics Nov 2008 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

 

BA 17

 

FIFTH SEMESTER – November 2008

ST 5404 – ACTUARIAL STATISTICS

 

 

 

Date : 12-11-08                       Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

PART-A

Answer ALL the questions:                                                                                         (10×2=20 marks)

 

  1. Define immediate perpetuity, perpetuity due.
  2. The amount with compound interest of a certain principal at 5% pa is Rs3969. Find the  principal

when the period is 2 years.

  1. Find the nominal rate p.a convertible half-yearly corresponding to an effective rate of  8% p.a.
  2. The accumulated value of a certain annuity paid after 8 years at the rate of 8% is 2866.35.  Find the

present value.

  1. Explain deferred annuity due.
  2. Define Lx .
  3. Explain Ax .
  4. Explain the need for a life table.
  5. What is the need for a commutation function ?
  6. Expand Sx in terms of Dx  .

 

PART-B

Answer FIVE questions:                                                                                             (5×8=40 marks)

 

  1. 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?

  1. Derive the formula for accumulated value and present value of annuity certain due.
  2. Derive the formula for an increasing annuity .
  3. 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.

  1. 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.

  1. Obtain the expressions for a x: n and  ( Ia )x : n   .
  2. 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.

  1. Obtain the formula for an and Sn.

 

 

 

PART-C

Answer TWO questions:                                                                                        (2×20=40 marks)

 

  1. a) Complete the following life table.

 

Age                   lx                dx              qx               Lx

10               1000000             –            .00409             –

11                    –                     –           .00370              –

12                    –                     –           .00347              –

13                    –                     –           .00342              –

 

  1. 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

  1. 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.

 

  1. 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?

 

  1. 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.

 

  1. 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.

 

  1. b) Derive the expression for 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.

 

  1. 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).

 

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