POLICY STRUCTURE

The insurance company has now decided on the product structure it wants for its policy. The structure is as follows:

• Whilst alive, policyholders pay annual premiums of at Year 0, 1, 2, , 1.
• If the policyholder dies, the policyholders dependent(s) receive a claim at the end of the year of death equal to a return of aggregate premium payments without interest.
• Upon survival until Year , policyholders receive a claim at Year .

Unless told otherwise, for the remaining questions assume that interest rates each year on Actual Reserves follow a normal distribution with a mean of 4% and a standard deviation of 5%, and that =$300,000 and =25. The product is sold to 10,000 policyholders aged exactly 40 at Year 0.

Don't forget to use the life table for all remaining questions, unless told otherwise.

1) Calculate the expected present value (EPV) of the claims for an individual policyholder for the above policy as a function of . Assume an interest rate for the calculation of reserves of 4% per annum.

Note that your answer will be in the form +.

= (to 5 decimal places)

= (to 2 decimal places)

2) Calculate the value of the premium (to 2 decimal places) to be charged to ensure that the EPV of claims (from1) is equal to the EPV of premiums.

3) Calculate the probability (to 3 decimal places) that an annual premium of $7,500 will be sufficient to cover all future claims cash flows.

4) All other things remaining equal, what impact would a value of =5% instead of =4% have on the probability that the annual premium of $7,500 will be sufficient to cover all future claims cash flows, as calculated in 3 ?

A)The probability of sufficiency is higher when =5% compared to =4%

B) The probability of sufficiency is unchanged when =5% compared to =4%

C) The probability of sufficiency is lower when =5% compared to =4%

5) Calculate the annual premium to be charged (to the nearest whole dollar) to give a 95% probability of being sufficient to cover all future claims cash flows.

6) For an annual premium of $7,500, calculate the Expected Reserves (to 2 decimal places) at Year 20 (after the payment of the premium at Year 20) for a single alive policyholder who purchased this policy at age 40. Assume a fixed interest rate on reserves of 4% per annum.

7) The insurer now wishes to take money from the Actual Reserves whenever the Actual Reserves exceeded the Expected Reserves by more than 20%. From Year 5 up until and including Year of the policy, the insurer will take away any money in the Actual Reserves that is greater than 1.2 x Expected Reserves, except where the Expected Reserves are negative, in which case the Actual Reserves are set to zero.

For an annual premium of $7,500, calculate the value of such that the probability that the premium will be sufficient to cover the claims cash flows is 55%. Note that should be an integer.

NOTE:(PLEASE GIVE ME YOU EMAIL TO SEND YOU THE LIFE TABLE)