MTH 217
1st SEMESTER 2024/25 Assignment 1&2
Life Insurance Mathematics I
Assignment 1&2
Q 1. Consider a fully discrete 20-year endowment insurance with sum insured $100 000, issued to a select life aged
40. Initial expenses are 3% of the sum insured and 20% of the first premium, and renewal expenses are 3% of the second and subsequent premiums.
Basis :
Mortality: IFoA Table AM92 Select
Interest: 6% per annum
(i) Write down an expression for the gross loss at issue random variable.
(ii) Calculate the gross annual premium.
(iii) Calculate the probability that the contract makes a profit.
Round your final solutions to 3 decimal places.
Q 2. An insurance company issues a whole life insurance policy to a life aged 60. The death benefit in the first five years of the contract is $1000. In subsequent years the death benefit is $50 000. The death benefit is payable at the end of the year of death and level premiums are payable annually throughout the term of the contract.
Basis for premiums and policy values:
Survival model: IFoA Table AM92 Select
Interest: 4% per year efective
Expenses: None
(i) Calculate the premium for the contract.
(ii) Write down the policy value formula for any integer duration t ≥ 5. (iii) Calculate the policy value at duration t = 5.
(iv) Use the recurrence relation to determine the policy value at duration t = 4.
(v) The insurer issued 1000 of these contracts to identical, independent lives aged 60. After four years there are 965 still in force. In the following year there were nine further deaths in the cohort, and the rate of interest earned on assets was 5.5%. Calculate the profit or loss from mortality and interest in the year.
Round your final solutions to 2 decimal places.
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