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

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.?
Find the nominal rate p.a convertible quarterly corresponding to an effective rate of 6% p.a.
Define a perpetuity due, immediate perpetuity .
Write the formula for (Ia)_n.
Express e_x in terms of l_x .
What is ?
Show that
What is double endowment assurance?
Write the formula for net interest yield of a life insurance company.
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

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?

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.
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.
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.
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
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.
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).
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)

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 10^th 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.
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.
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 5^th 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).
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.

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