Loyola College M.Sc. Statistics April 2006 Actuarial Statistics Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 38

SECOND SEMESTER – APRIL 2006

                                                     ST 2953 – ACTUARIAL STATISTICS

 

 

Date & Time : 26-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

PART-A

ANSWER ALL QUESTIONS                                                                       10 ´ 2 = 20

 

  1. A has invested Rs.1000 in National Defence savings certificate. After 15 years he is entitled to receive Rs.1750. What rate of interest is realized in the transaction.?
  2. Find the nominal rate p.a  convertible quarterly corresponding to an effective rate of 6% p.a.
  3. Define a perpetuity due, immediate perpetuity .
  4. Write the formula for (Ia)n.
  5. Express ex in terms of  lx     .
  6. What is ?
  7. Show that
  8. What is double endowment assurance?
  9. Write the formula for net interest yield of a life insurance company.
  10. Given a complete table of  for all values of x and n , how would you find the value of ?

Part-B

ANSWER ALL QUESTIONS                                                                         5 ´ 8 = 40

 

  1. A has taken a loan of Rs.2000 at a rate of interest 4% p.a payable half-yearly. He    paid 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. Find the amount of an annuity due of Rs. 300 p.a. payable 12 times a year for 20 years , on the basis of nominal rate oa 6%p.a. convertible 3 times a yaer. Find also the present value of these payment.
  2. Three persons are aged 30,35,40 respectively.Find the probability that                   One of them dies before age 45 While the others survive to age 55.                    ii. None of them dies before age 50.                                                                           iii. Atleast one of them attains age 65.                                                                     iv. None of them  survives upto age 65.
  3. Find the present value of an annuity due of Rs.1000 p.a. for 20 yeare if the rate of interest is 8% p.a. for the first 12 years and 6% p.a. there after. Find also the accumulated value.
  4. Calculate net annual premium under a special endowment assurance for Rs.18000 on (35) for 25 years, the premium being limited to 20 years. In the event of death during the term of assurance, total premium paid are returnable and on survivance to the end of 25 years, the basic sum assured becomes
  5. Calculate office annual premium for a whole life assurance for Rs. 20000 to a person aged 40. provide for first year expenses at 55% of premiums 17 per thousand sum assured; and renewal expenses of 5% of premium and 6 per thousand sum assured.
  6. Calculate the net single premium for an immediate annuity of Rs.1200 per annum payable half yearly in arrear for 15 years certain and thereafter for life to a person aged 60 at entry (basis: a(90) table and 8% interest).
  7. Calculate the net annual premium under a children deferred whole life assurance

for Rs 5000 on the life of a child aged 8,the assurance vesting at age 18.

 

                                           PART-C

ANSWER ANY TWO QUESTIONS                                       (2 ´ 20 = 40)

  1. a) A loan of Rs 5000 is to be repaid with interest at a rate of 6% p.a. by 18 level annual payment being made at the end of the first year. Immediately after the  10th payment has been made the borrower requests the lender for extension of the term of the loan by  another four years. What is the revised annual payment to be made during the next 12 years on the assumption that the lender to realise an interest of 7% hence forward?                                                                                                                 b) payments of i.  50/ at the end of each half year for the first 5 years followed by ii.  Rs.50/ at the end of each quarter for the next years, one made in to account to which interest is credited at the rate of 9% p.a. convertible half yearly. Find the accumulated value at the end of 10 years.
  2. a) Derive an expression for                                                                                                                        ii.                              iii.                                        b) A special  policy provides for the following benefits;                                                        i.  An initial sum of Rs.10,000 with guaranted annual additions of Rs.250 for each year’s 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 Rs.10,000 at death after expiry of the term of assurance.                                                                                                          calculate net annual premium under the policy on the life of (35) for 25 years.
  3. a) A person aged 30 years has approached a life for a special type of policy providing for the following benefits;                                                                            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 survivance to 20 years.                                            v. Rs.150 paid for each premium paid.   Calculate the yearly premium assuming the paying term is 20 years.                                                                                          b) Derive the formula for decreasing temporary assurance (mortgage  redemption assurance).
  4. a) Derive the formulas for net premiums of the various life annuity plans. b) calculate office annual premium for an endowment assurance for Rs.15,000 to a person aged 35 for 25 years. provide for first year expenses at 50% of premium and 15 per thousand sum assured; and renewal expenses of 5%of premiums and 6 per thousand sum assured. A bonus loading of 20 per thousand is also offered. Calculate the office annual premium.

 

Go To Main Page

Loyola College M.Sc. Statistics April 2007 Actuarial Statistics Question Paper PDF Download

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.

  1. Given Sn how will you find an ?

Given an how will you find Sn ?

  1. Find the nominal rate per annum convertible quarterly corresponding to an effective rate of 9%.
  2. Define e
  3. Given a complete table of ax:n how will you find Ax:n..
  4. Expand Rx in terms of Cx.
  5. Explain double endowment assurance.
  6. 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?
  7. Distinguish between a perpetual annuity and a life annuity.

 

PART-B

 

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

 

  1. 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?

  1. 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.

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

Arithmetic progression.

  1. 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.

  1. 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.

  1. 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.

 

 

 

 

 

  1. 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 15th payment he closes his account, What is the  amount payable to him if interest is allowed at 9% pa?
  2. Derive the formulae for

ax: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 10th payment.Immediately after the 10th 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.

  1. Explain the stages in the construction of life table in detail.
  2. a)Derive the formula for

an, S

            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)

 

Go To Main Page

Loyola College M.Sc. Statistics Nov 2012 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2012

ST 3956 – ACTUARIAL STATISTICS

 

 

Date : 08/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Section – A

 

Answer all the questions:                                                                                                        ( 10 x 2 =20)

 

  1. Find the present value at rate of interest 7% p.a. of Rs.500/-payable in 4 years and months.
  2. What is discount?
  3. Define deferred annuity and deferment period.
  4. Write the formula for the present value of increasing annuity wherein the successive instalment from a geometric distribution.
  5. Define expectation of life and write and expression for ex.
  6. What is meant by Whole Life Assurance?
  7. Prove that A x:n = D x + n / Dx
  8. What is the benefit that is represent by a x : n – a x : n-1?
  9. What are the defects in the system in the system of charging natural premiums?
  10. Given that Ax =0.7115 and a x = 6.5 determine the rate of interest.

 

Section –B

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

 

  1. a) Find the effective rate p.a. corresponding to the nominal rate of 8% p.a. convertible quarterly.
  2. b) Find the nominal rate p.a. convertible quarterly corresponding to an effective rate of 8% p.a.
  3. A has taken a loan of Rs. 2000 at a rate of interest 4% p.a. 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 transactions. What was the final payment

made by him?

  1. A has right to receive an amount of Rs.1000 at the end of 12 years from now. This right has been sold to B for a present value calculated at the rate of 8% p.a. The money thus received was invested by A in deposit account at 9% p.a. payable half yearly. After 8 years the account had to be closed and A then invested the amount available at 6% p.a. in another bank. How has A gained or lost in this transaction, as at the end 12 years?
  2. Derive an expression to find accumulated value of deferred annuity due.

 

  1. Find the following probabilities:
  • a life aged 35 will die between that ages 45 and 50
  • a life aged 35 will not die between that ages 45 and 50
  • a life aged 35 will die in the 10th year from now.
  • a life aged 35 will not die in the 10 year from now.

 

  1. Describe the relative advantages and disadvantages of the policy year method as against life year method and calendar year method.

 

  1. Using commutation functions based on LIC ( 1970 -1973) Ultimate mortality table at 6% interest. Calculate for a person aged 40;
  2. The present value of whole life assurance of Rs.10,000/-
  3. The present value of double endowment assurance of Rs.10,000

for 15 years term. Also calculate the present value of endowment assurance and the pure endowment each for Rs.10, 000 for 15 years term.

  1. Derive an expression for Increasing Temporary life annuity.

 

Section – C

 

Answer any two questions:                                                                                                   ( 2 x 20 = 40 )

 

  1. a) The cash purchase price of a bike is Rs. 10,000. A company however offers instalment plan where under an immediate payment of Rs. 2000 is to be made and a series of 5 equal half-yearly payments made thereafter, the first installment being payable at the end of 6 months. If the company wishes to realize a rate of interest of 12 % convertible half-yearly in the transaction, calculate the half-yearly instalment.

 

  1. b) A fund is to be set up out of which a payment of Rs.100 will be made to each person who in any year qualifies for membership of a certain procession. Assuming that 10 person will qualify at the end of one year from now, 15 at the end of 2 years, 20 at the end of 3 years, and so on till the number of qualifiers is 50 per annum. When it will remain constant? Find at 5% p.a. effective. What sum must be paid in to the fund now so that it sufficient to meet the outgo?

 

  1. a) A loan of 16,000/- is repayable by level instalment of principal and interest, payable  yearly in arrears over 15 years. The rate of interest is 8% p.a. for the first 6 years and 7% p.a. thereafter. Calculate the level yearly instalment and interest contained in the 1st, 2nd, 9th & 10th instalment.
  2. b) Of three person A, B and C, aged 40, 45 and 50 respectively, find the probability that at least one of them will not die between the ages 65 and 70.

 

  1. Explain in detail the stages in the construction of the life table.

 

 

  1. a) The following particulars are given:
x 25 26 27 28 29 30
lx 97380 97088 96794 96496 96194 95887
dx 292 294 298 302 307 313

 

 

 

 

Calculate ignoring interest, allowing interest @ 6 % and expenses:

  • The value of temporary assurance of Rs. 1000 for 2 years for a person aged 25.
  • The value of endowment assurance benefit of Rs. 1000 for 4 years to a person aged 25.

 

  1. b) Prove that  = n  ax

 

 

Go To Main Page

 

 

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).

 

Go To Main Page

Loyola College B.Sc. Statistics April 2009 Actuarial Statistics Question Paper PDF Download

      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 23

FIFTH SEMESTER – April 2009

ST 5404 – ACTUARIAL STATISTICS

 

 

 

Date & Time: 28/04/2009 / 1:00 – 4:00       Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

 

ANSWER ALL THE QUESTIONS                                                             (10  x 2 = 20)

 

  1. Find the present value of Rs. 1000 receivable at the end of 50 years the rate of interest being 5% p.a.
  2. Write the formula for finding effective rate of interest given the nominal rate of interest.
  3. Write the two relations between  and .
  4. Define the two types of perpetuity.
  5. Explain  , .
  6. Define and .
  7. Explain life annuity, temporary life annuity.
  8. Explain the principle of life insurance.
  9. Explain the pure endowment assurance.
  10. Define the office premium.

PART – B

 

ANSWER ANY FIVE QUESTIONS                                                             (5 x 8 = 40)

 

  1. Two loans of Rs.500 each are made out to A three years ago and 2 years ago respectively and an interest of 6% p.a. was agreed upon.  At present A could make a repayment of Rs. 400.  He promises to clear the dues at the end of 2 years from now.  How much will he have to pay then?
  2. Derive the formula for  and .
  3. A has taken a loan of Rs.10,000.  He pays the level annual payment at the end of each year for 5 years.  What is the installment amount? What is the amount towards the principle in the third payment?  What is the principal outstanding at the end of 3 years?
  4. Find the accumulated value of an annuity due of Rs. 400 p.a. payable in equal quarterly installments for 12 years certain at nominal rate of interest of 7% p.a. convertible half yearly.
  5. Find the probability that
  • a life aged 35 will die between 45 and 50
  • a life aged 35 will die after 60
  • a life aged 35 will die in the 10th year from now.
  • A life aged 35 will survive another 10 years.
  1. On the basis of LIC table at 6% calculate the net annual premium ceasing after 15 years or at previous death for money back policy on (45) to secure the following benefits.
  • 1500 on survivance to the end of 5 years.
  • 1500 on survivance to the end of 10 years
  • 3000 on survivance to the end of 15 years
  • 6000 on death at any time within 15 years
  1. Derive the formula for present value when the successive instalments form an arithmetic progression.
  2. Explain the various types of life annuities.

PART – C

 

ANSWER ANY TWO QUESTIONS                                                           (2 x 20 = 40)

 

  1. a). Payments of (i) Rs 50 at the end of each half-year for the first 5 years followed by (ii). Rs 50 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% p.a. convertible half-yearly.  Find the accumulated value at the end of 10 years.

b). Provident fund (PF) deductions are made at the rate of Rs. 200 per month.                   Find the accumulated value at the end of 10 years, at a rate of interest 10% p.a.

( 10 + 10)

  1. a). Derive the formula for ,

b). A special policy provides for the following benefits.

(i). An initial sum of Rs. 10,000 with guaranteed annual additions of Rs.250                            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 and

(iii). Free paid up assurance of Rs.10,000 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.                                                    ( 10 + 10)

  1. a). Complete the following life table
Age
35 86137 742 .00842
36 .00885
37
38
39 .00969

b). Three persons are aged 30,35,40 respectively.  Find the probability that

(i). One of them dies before 45 while the others survive to age 55.

(ii). Atleast one of them attains age 65.

(iii). All of them die after 70.

(iv). None of them reach age 70.

(v). exactly 2 of them die before 45 and one survive to age 60.    ( 10 + 10)

  1. Write short notes on any three of the following

(i). Children deferred assurances  (ii). Double endowment assurances.

(iii). Equation of value                  (iv).  and

(v). Present value of perpetuities.                                         ( 10 + 10)

 

  Go To Main page

Loyola College B.Sc. Statistics April 2012 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

ST 5404 – ACTUARIAL STATISTICS

 

 

Date : 27-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

 

ST-5404  actuarial STATISTICS                  MAX: 100 Marks     

Section – A

                                                  (Answer all the questions)                                    (10 x2 =20)

 

  1. What is the present value of Rs.5,000 receivable at the end of 75 years, the rate of interest being taken as 6 % p.a?
  2. Find the nominal rate p.a convertible quarterly corresponding to an effective rate of 8% p.a.
  3. Show that
  4. Give the formula for an and Sn
  5. Evaluate v60 @ 6.2%
  6. Write an expression 10P42, 10 │ 5P
  7. Define d
  8. What is a temporary assurance?
  9. What is the need for a commutation function?
  10. Expand Sx in terms of  Dx

 

Section – B

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

 

  1. A sum of Rs.2000 is invested at a rate of interest of 5%p.a. After 7 years, the rate of interest was changed to 5% p.a. convertible half yearly. After a further period of 3 years, the rate was again changed to 6%p.a. convertible quarterly. What is the accumulated value at the end of 15 years from the commencement?

 

  1. Define the following:
  • Annuity
  • Immediate annuity
  • Annuity due
  • Deferment period

 

  1. Calculate the present value of a deferred annuity payable for 10 years certain, the first payment falling due at the end of 6 years from the present time. The annuity is payable at the rate of Rs. 100 p.a. for the first 5 years and Rs.200 p.a. thereafter.

(a5 = 4.3295,  a10 = 7.7217,  a15 = 10.3797)

 

  1. A fund is to be set up out of which a payment of Rs.100 will be made to each person who in any year qualifies for membership of a certain profession. Assuming that 10 persons will qualify at the end of one year from now, 15 at the end of 2 years, 20 at the end of 3 years, and so on till the number of qualifiers is 50 per annum. When it will remain constant, find at 5% p.a. effective what sum must be paid into the fund now so that it sufficient to meet the outgo.

 

 

  1. Derive the expression to find the present value and accumulated value of Increasing

annuity where in the successive installment form  a geometric progression.

 

  1. Find the office annual premium for a capital redemption assurance policy of Rs. 3000 redeemable at the end of 20 years, assuming interest rate of 6% and a loading of 8% of office premium.

 

  1. Using the LIC ( 1970 – 73 ) Ultimate table find the following  probabilities

 

  • that a life aged 35 dies within 12 years
  • that a life aged 40 dies not earlier than 12 years and not later than 15 years
  • that a life aged 52 survive 12 years
  • that a life aged 52 will not die between age 65 and 70      ( 2+2+2+2)

 

  1. Explain Pure Endowment Assurance.

 

 

Section – C

                                                   (Answer any two questions)                               ( 2 x 20 =40)

 

  1. Explain the various types of annuity and derive the expression for present value and accumulated value of an immediate annuity certain and deferred annuity certain.

 

  1. a)A deposit annually Rs. 200 p.a. for 10 years, the first deposit being made one year from now; and after 10 years the annual deposit is enhanced to Rs. 300 p.a. Immediately after depositing the 15 payment he closes his account. What is the amount payable to him if interest is allowed at (i) 6% p.a. (ii) 9% p.a.?
  2. b) What is the principle of insurance? How has endowment type assurance

emerged?

 

 

 

  1. a) Fill in the blanks in the following portion of a life table
Age  X lx dx qx px
10 1000000   0.00409  
11     0.00370  
12       0.99653
13       0.99658
14     0.00342  

 

 

 

 

 

 

 

  1. b) Using commutation function based on LIC ( 1970 – 73) ultimate mortality table at 6% interest calculate for a person aged 40

 

  • The present value of Whole Life Assurance of 10000
  • The present value of Double Endowment Assurance of 10000

 

for 15 years term . Also calculate present value of Endowment Assurance and Pure Endowment of each for Rs. 10000 for 15 years term.

 

  1. a) Explain Rx ,Mx,Dx and obtain expression for ( IA) x : n

 

b)The following particulars are given:

X 25 26 27 28 29 30
lx 97380 97088 96794 96496 96194 95887
dx 292 294 298 302 307 313

 

Calculate ignoring interest and expenses:

  • The value of Temporary Assurance of Rs. 1000 for 2 years for a person aged 25.
  • The value of Endowment Assurance benefits of Rs. 1000 for 4 years to a person aged 25.
  • The value of a Pure Endowment of Rs. 600 for a person aged 27 receivable on attaining age 30.

 

 

Go To Main page

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Loyola College B.Sc. Statistics Nov 2012 Actuarial Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2012

ST 5404 – ACTUARIAL STATISTICS

 

 

Date : 10/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

Section – A

Answer all the questions:                                                                                                     ( 10 x 2 = 20)

 

  1. The amount with compound interest of a certain principal at 5% p.a. is Rs. 3969. Find the principal when period is 2 years.
  2. What is meant by discount?
  3. What is the effective rate p.a. corresponding to a nominal rate of 8 % p.a. convertible monthly?
  4. Evaluate v9 s13 @ 9 %
  1. Define an annuity.
  1. Show that
  2. What is perpetuity due?
  3. Define q
  4. Give the expression for e
  5. Write a short note on term assurance.

Section – B

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

 

  1. The amounts for a certain sum with compound interest at a certain rate in two years and in three years are Rs. 8820 and Rs. 9261 respectively. Find the rate and sum.
  1. A has taken a loan of Rs. 2000 at a rate of interest 4% p.a. 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?
  2. The cash purchase price of a bike is Rs. 10,000. A company however offers instalment plan  under an immediate payment of Rs. 2000 is to be made and a series of 5 equal half-yearly payments made thereafter, the first installment being payable at the end of 6 months. If the company wishes to realize a rate of interest of 12 % convertible half-yearly in the transaction, calculate the half-yearly instalment.
  1. Calculate the present value of a deferred annuity payable for 10 years certain, the first payment falling due at the end of 6 years from the present time. The annuity is payable at the rate of Rs. 100 p.a. for the first 5 years and Rs.200 p.a. thereafter.

Given (a5 = 4.3295,  a10 = 7.7217,  a15 = 10.3797)

  1. Derive the formula for accumulated value and present value of annuity certain due.
  2. Using the LIC ultimate table find the following probabilities:
    1.  a life aged 35 dies within 12 years.
    2.  a life aged 40 dies not earlier than 12 years and not later than 15 years.
    3.  a life aged 2 survives 12 years
  1. a life aged 52 will not die between ages 65 and 70

 

  1. What are the points to be borne in mind in deciding
  • Period of investigation?
  • Period of selection?
  • Method to be used for investigation?
  1. Derive an expression for A x:n.

Section – C

Answer any two questions:                                                                                                 ( 2 x 20 =40)

 

  1. a) A has right to receive an amount of Rs.1000 at the end of 12 years from now. This right has been sold to B for a present value calculated at the rate of 8% p.a. The money thus received was invested by A in deposit account at 9% p.a. payable half yearly. After 8 years the account had to be closed and A then invested the amount available at 6% p.a. in another bank. How has A gained or lost in this transaction, as at the end of 12 years?

 

  1. b) Derive an expression to find the present value for the following variable annuities:
  2. Increasing annuity
  3. Immediate Increasing Perpetuity
  • Increasing annuity due
  1. Increasing Perpetuity due
  2. a) A loan of Rs. 3000 is to be repaid with interest at 6% p.a. by means of an immediate annuity for 10 years. Find the level payment. What will be the interest and principal contained in the 5th instalment? What will be the principle outstanding immediately after the 8th payment is made?

( 10 + 10)

  1. b) In lieu of a single payment of Rs. 1000, at the present moment a person agrees to receive 3 equal payments at the end of 3 years, 6 years and 10 years respectively. Assuming a rate of interest of 6% p.a. what should be the value of each of the 3 payments? ( 10 + 10)

 

 

  1. a) Write down expression for probability  in the under mentioned cases:

(i)  Life aged 25 dies between ages 60 and 65

(ii)  Of the two life aged 25 and 30, at least one life dies before attaining age 70

(iii)  Of three lives aged 40, 40 and 45, exactly two lives survive 10 years

(iv) Life aged 28 survives 12 years and dies in the 13th, or 14th year.

 

  1. b) Fill up the blanks in the following portion of a life table:
       Age  X lx dx qx px
10 1000000 0.00409
11 0.00370
12 0.99653
13 0.99658
14 0.00342

 

( 10 + 10)

  1. a) A person aged 30 years has approached a life office for special type of policy providing for the following benefits:
  • 1000 on death during the first 5 years
  • 2000 on death during the next 5 years
  • Survival benefit of Rs. 500 at the end of the 5th year
  • Further payment of Rs. 2000 on survivance to 20 years.
  • An annuity of Rs. 200 per annum payable in his life time, the first such payment falling due along with the survival benefits of Rs. 2000.

 

  1. b) Derive the expression for Ax and (IA) x : n. ( 10 + 10)

 

 

Go To Main page

 

 

 

 

 

 

 

 

 

 

 

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur