LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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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)
- Find the present value of Rs. 1000 receivable at the end of 50 years the rate of interest being 5% p.a.
- Write the formula for finding effective rate of interest given the nominal rate of interest.
- Write the two relations between and .
- Define the two types of perpetuity.
- Explain , .
- Define and .
- Explain life annuity, temporary life annuity.
- Explain the principle of life insurance.
- Explain the pure endowment assurance.
- Define the office premium.
PART – B
ANSWER ANY FIVE QUESTIONS (5 x 8 = 40)
- 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?
- Derive the formula for and .
- 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?
- 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.
- 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.
- 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
- Derive the formula for present value when the successive instalments form an arithmetic progression.
- Explain the various types of life annuities.
PART – C
ANSWER ANY TWO QUESTIONS (2 x 20 = 40)
- 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)
- 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)
- 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)
- 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)
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