(Papers) ACET Paper May 2010 "CT5 – General Insurance, Life and Health Contingencies"

Q. 1) If ‘T’represents the present value of a temporary annuity due with a term of n years, derive the variance of ‘T’ in terms of assurance functions for a life aged x.

Q. 2) What is meant by “direct expenses” incurred by a life insurance company in respect of a life insurance contract? Describe three different categories of direct expenses and give an example of each.

Q. 3) A life insurer issues 20-year term assurance policies to lives aged 45 exact. The sum assured, which is payable immediately on death, is Rs. 5,00,000 for the first 10 policy years, and Rs. 1,00,000 thereafter. Level annual premiums of Rs.1897.24 are payable for 20 years or until death, if earlier.

i) Find the prospective reserve at the end of 10th policy year.
ii) Using your answer to part (i), describe the disadvantages to the insurer after 10th policy year for selling these policies. Suggest any two changes in the product design so as to remove the disadvantages?

Following bases is used to calculate the premiums and reserves:

Mortality: AM92 Ultimate
Interest: 4% per annum
Expenses: nil.

Q. 5) A level premium with-profit 20-year endowment assurance policy, issued to a life aged exactly 40 has a sum assured of Rs. 10,000. the death benefits are payable at the end of the year of death. Premiums are calculated assuming AM92 Select mortality, 4% pa interest, initial expenses of Rs.150 and claim related expenses of 3% of the base sum assured (payable on death or maturity).

Calculate the annual premium if the policy is assumed to provide compound bonuses of 4% pa of the sum assured vesting at the end of each policy year.

Q. 6) A life insurance company issue a 5 year unit linked pension plan to a life aged 45 exact on 1st Jan 2009 under which level premiums are payable yearly in advance. 95% of the premiums are allocated to units in all five policy years. A fund management charge of 2.5% of the fund value is deducted at the end of each policy year. A fixed administration charge of Rs 720 p.a. is deducted at the start of each policy year.

The management charges are deducted from the fund before any death benefits are paid.

The death benefit is equal to the fund value and the benefits are paid only at the end of the year.

The investment managers follow a passive investment strategy which mimics the nifty index.

The Company uses the following assumptions in its profit test for this policy:

a. Calculate the account value at the end of five policy years showing detailed calculations assuming annual premium is Rs.1,00,000.

b. The product also guarantees on maturity a 2.5% return per annum compounded on the premiums paid. Therefore the maturity value is equal to the higher of fund value at maturity or the guaranteed amount at maturity. Calculate the Value of new business assuming an RDR of 12%. Value of new business is equal to the present value of profits divided by the annual premium.

c. The Chief Actuary now decides to build up a reserve for the guaranteed payout equal to 2.5% of the year end fund value in the first four policy years. This reserve would be released in the fifth policy year to meet the guarantee, if required. Recalculate the value of new business allowing for this new requirement.

d. Calculate the IRR to the customer based on assumptions available at the time of pricing the product.