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MTH 217

1st SEMESTER Assignment Sample

BSc. Actuarial Science

Life Insurance Mathematics I

Assignment Sample

Q 1. A select life aged exactly 40 has purchased a deferred annuity policy. Under the terms of the policy, the annuity payments will commence 20 years from the issue date and will be payable at annual intervals thereafter. The initial annuity payment will be $50 000, and each subsequent payment will be 2% greater than the previous one.

The policy has annual premiums, payable for at most 20 years.

The life insurance company uses the following basis for calculating premiums and reserves:

Mortality: The Life Table in the Enclosed EXCEL

Interest: 5% per annual

Initial Expense: are 2.5% of the first annuity payment and 20% of the first premium.

Renewal Expense: are 5% of the second and subsequent premiums

Terminal Expense: incurred at the end of the year of death, are $20 inflated from the issue date, assuming an inflation rate of 3% per year.

Calculate the gross premium. In order to perform the calculation, create columns showing:

• the amount of annuity payments made in year t

• the amount of terminal expenses made in year t

• the probability of the annuity payments and premiums being made.

• the probability of terminal expenses being made.

• the amounts by which that cash flows is discounted

• how to obtain the EPV of annuity payments

• how to obtain the EPV of annual premiums for unit amount per year.

Please complete your calculation in the answer sheet of enclosed excel file. Please notice: you are allowed to add or delete columns or lines if you need, but the green columns and the final answer in yellow cell are mandatory.