On 1 January 2013 a life insurance company issued a number of whole life insurance policies with sum insured $100,000 to select lives then aged 40. Level premiums are paid annually in advance and the death benefit is paid at the end of the year of death.

The premium is calculated using the AM92 select tables and assuming

• Interest: 4%

• Initial expenses: $200 plus 40% of the first gross premium

• Renewal expenses: 5% of gross premium due at the start of each policy year from the second year onward

1. Calculate the gross premium.

2. Calculate the net premium policy value at t = 2 using the premium basis.

3. Calculate the gross premium policy value at t = 2 using the premium basis.

4. Explain why the gross premium policy value is less than the net premium policy value in this case.

5. There were 1000 policies in force on 1 January 2015. During 2015, there were 4 actual deaths and the actual interest rate earned by the company was 5.5%. The actual expense follows the assumption. Calculate the profit or loss by the company in respect of these policies for the year 2015.

6. Analyse the profit or loss into components for interest and mortality.