Question 1

A life insurance company issues a number of 3-year term assurance contracts to lives aged

exactly 60. The sum assured under each contract is 200,000, payable immediately on death.

Premiums are payable annually in advance for the term of the policy, ceasing on earlier death.

The company carries out profit tests for these contracts using the following assumptions:

Initial expenses: 200 plus 35% of the first year's premium

Renewal expenses: 25 plus 3% of the annual premium, incurred at the beginning of the

second and subsequent years

Mortality: AM92 Ultimate

Investment return: 7% per annum

Risk discount rate: 15% per annum

Reserves: One year's office premium

(i) Show that the office premium, to the nearest pound, is 2,610, if the net present value of

the profit is 25% of the office premium.

(ii) Calculate the expected in-force cashflows if the company holds zero reserves throughout

the contract, using a premium of exactly 2,610.

(iii) Explain why the company might not hold reserves for this contract and the impact on

profit if it did not hold any reserves.

A profit test for unit-linked policies issued to lives aged 60 has been carried out. The expected non-unit cashflows before setting up non-unit reserves are as follows: Year Expected non-unit cashflows per policy in force at start of year -30 2 -12 3 -6 4 20 5 30 Write down an expression for the expected loss at the end of Year 1, after zeroisation of all negative cashflows. A conventional 3-year endowment assurance is issued to a life aged exactly 56. The details are: sum assured 10,000 payable after 3 years or at the end of the year of death, if earlier surrender value equal to the return of premiums without interest, less 400, at the end of the year of surrender annual premium 3,250 paid at the start of each year. The company calculates its reserves for this contract on the following basis: Expenses: 30 at the start of Year 2 32 at the start of Year 3 Surrender probabilities: 4% of policies in force at the end of Year 2 only Mortality: AM92 Ultimate Interest: 2% pa (i) Calculate the prospective gross premium reserves required per policy in force at the start of Years 2 and 3, according to the above basis, using a cashflow projection approach. (ii) Calculate the expected profit arising in the second year per policy in force at the start of Year 2, assuming the following profit test experience basis: Expenses: as reserving basis Surrenders: as reserving basis Reserves: as calculated in part (i) Mortality: 75% of AM92 Select from policy outset Interest: 4% pa (iii) Explain why the expected profit calculated in part (ii) is not zero.You are given the following select and ultimate mortality table: X ( x] [ x ]+1 1( x1+2 4 x]+3 1x+4 51 1,537 1,517 1,502 1,492 1,483 52 1,532 1,512 1,497 1,487 1,477 53 1,525 1,505 1,490 1,480 1,470 54 1.517 1,499 1,484 1,474 1,462 55 1,512 1,492 1,477 1,467 1,453 (i) Calculate the probability that a life selected at age 51 and still alive at age 53 will survive to age 55. [1] (ii) Given that d 55:101 =8.078 when i = 0.04, calculate the corresponding select mortality annuity, do . Comment on your answer. [5] [Total 6]