LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AC 37

M.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2007

ST 2953 – ACTUARIAL STATISTICS

 

 

 

Date & Time: 24/04/2007 / 1:00 – 4:00      Dept. No.                                       Max. : 100 Marks

 

 

 

PART-A

 

Answer all the questions                                 (10×2=20)

1. Define immediate annuity certain and annuity certain due.
2. A has invested Rs1000 in NSC. After 15 years he is entitled to get Rs1750.What rate

of interest is realized in the transaction.

3. Given S_n how will you find a_n ?

Given a_n how will you find S_n ?

4. Find the nominal rate per annum convertible quarterly corresponding to an effective rate of 9%.
5. Define e
6. Given a complete table of a_x:n how will you find A_x:n..
7. Expand R_x in terms of C_x.
8. Explain double endowment assurance.
9. A pays Rs500 at the end of every year for 10 years @ 8% per annum.What is the value of all these payments at the end of 6 years?
10. Distinguish between a perpetual annuity and a life annuity.

 

PART-B

 

Answer any 5 questions:                                            (5x 8 = 40)

 

11. A loan of 5000 is to be repaid by payments of Rs2500 at the end of 1 year ,Rs1500

at the end of 2 years  and the balance at the end of 4½ years. What should the final

payment be if interest is reckoned at 9% per annum convertible half-yearly?

12. PF deductions are made monthly at a rate of Rs2000 per month and credited to PF

account. Find the accumulated value at the end of 10 years @ 10% pa.

13. Derive the formula for increasing annuity when the successive installments form an

Arithmetic progression.

14. Three persons are aged 30,35,40 respectively find the probability that

i)one of them dies before 45 while the others survive to 55.

ii)atleast one of them attains 65.

15. Calculate office annual premium for an endowment assurance for Rs15,000 to a

person aged 30 for 25years.provide for first year expenses at 50% of premiums and 15% sum assured; and renewal expenses of 5% of premiums and 6% sum assured.

16. Calculate the net annual premium under a children referred endowment assurance for

Rs25,000 on the life of a child aged 5 , the assurance being vested at the age 21 and maturing at age 55 .Calculate also the additional premium for the benefit  of  waiver  of premiums payable during the deferment period in the event of death of the childs father aged 39 at 6% interest.

 

 

 

 

 

17. A deposits annually Rs200 per annum for 10 years, the first deposit being made one year from now, and after 10 years the annual deposit is enhanced to Rs.300 per annum.  Immediately after depositing the 15^th payment he closes his account, What is the  amount payable to him if interest is allowed at 9% pa?
18. Derive the formulae for

a_x:n  and a _x:n

and decreasing temporary assurance.                                           (2+2+4)

 

PART-C

       Answer any two questions                                                       2×20=40

 

19.a).Aloan of Rs.7500 is to be repaid with interest at 8% per annum by means of level annual

payments, the first one being made at the end of first year . Find the principal

payments contained in the 10^th payment.Immediately after the 10^th payment  is

made the lender desires to have the balance repaid in 3 level annual payments

including  principal and interest; to which the borrower agreed provided a rate of

7% per annum is used for this agreement.Find the revised level payment.                       (15)

1. b) Under settlement of property A will recieveRs1800 per annum ad infinitum the first

payment being receivable at the end of 6 years from now .Find the present value of

A’s rights at 9% pa.                                                                                                             (5)

20.a) A special policy provides for the following benefits:

i)an initial sum of Rs10,000/- with guranteed annual additions of Rs250 for

each years premium paid after the first,if death occurs within the term of

assurance.

ii)Rs 10,000 payable on survivance to the end of the term of assurance.

iii)Free paid-up assurance of Rs10,000/- payable at death after expiry of the

term of assurance

Calculate net annual premium under the policy on the life of (35) for 25 years (12)

1. Calculate the net annual premium limited to 15 years for a temporary assurance on

(40) providing the following benefits.

i)Rs5000 on death during the first 5 years.

ii)Rs10,000 on death during the next 5 years.

iii)Rs15,000 on death during the last 10 years.

21. Explain the stages in the construction of life table in detail.
22. a)Derive the formula for

a_n, S_n 

            b)Payments of i)Rs50 at the end of each half year for the first 5years followed by

ii)Rs50 at the end of each quarter for the next 5 years are made into

an account to which interest is credited  at the rate of 9% per annum

convertible half yearly. Find the present value and accumulated

value at the end of 10 years.

c)A sum of Rs150 is deposited in a bank at the beginning of each year.What is the

amount to the credit of the depositor at the end of 20 years if inerest is credited

to the account at  6% for the first 10 years

7% for the next 5 years and

8% thereafter ?

(6+7+7)

 

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