Microeconomics questions

A special 25-year life insurance policy is issued to a life aged x and provides the

following benefits:

? a lump sum of 75,000 (payable at the end of the policy year) if death occurs

during the first 10 years

? a dependants' pension (payable in the form of an annuity certain) of 5,000 pa

payable on each remaining policy anniversary during the term (including the

25th anniversary) if death occurs after 10 years but before the end of the term of

the policy

? a pension of 7,500 pa commencing on the day after the term of the policy

expires and with payments on each subsequent policy anniversary while the

policyholder is still alive.

Write down an expression for the present value random variable of the benefits under

this policy.

Explain why a life insurance company might need to set up non-unit reserves in respect of a unit-linked life assurance contract. The following table shows (in f's) a profit testing calculation (with some of the entries missing) for three-year endowment assurance contracts issued to lives aged exactly 57 with a sum assured of 65,000 payable at the end of the year of death. Outgo terms are shown as negative entries. Expected Expected cost cost of death Profit Year Premium Expenses Interest of increasing and maturity vector reserves (* ) claims 1 1,530 -50 ? ? -51 2 1,530 ? ? 21 3 1,530 45 The mortality probability at each age is 1%. The rate of interest earned on cashflows and reserves is 6%. Reserves are calculated using an interest rate of 4%. The reserves are zero at the start and end of the contract. The interest earned on the reserve in the third year is f195. (i) Complete the table. (ii) Calculate the internal rate of return. (iii) Explain the effect that changing to a weaker reserving basis would have on the internal rate of return. (iv) Calculate the net present value using a risk discount rate of 7%. (v) Explain the effect that changing to a weaker reserving basis would have on the net present value. (* ) Allowing for interest earned on reserves