A whole life insurance with sum insured $100000 is issued to a select life aged 35. 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 Standard Select Survival Model, and assuming Interest: 6% per year effective Initial Expenses: 40% of the gross premium plus $125 Renewal expenses: 5% of gross premiums plus $40, due at the start of each policy year from the second onwards (a) Calculate the gross premium. (b) Calculate the net premium policy value at t = 1 using the premium basis. (c) Calculate the gross premium policy value at t = 1 using the premium basis. (d) Explain why the gross premium policy value is less than the net premium policy value. (e) Calculate the gross premium policy value at t = 1 assuming interest of 5.5% per year. All other assumptions follow the premium basis. (f) Calculate the asset share per policy at the end of the first year of the contract if experience exactly follows the premium basis. (g) Calculate the asset share per policy at the end of the first year of the contract if the experienced mortality rate is given by 935) = 0.0012, the interest rate earned on assets was 10%, and expenses followed the premium basis, except that there was an additional initial expense of $25 per policy. (h) Calculate the surplus at the end of the first year per policy issued given that the experience follows (f) and assuming the policy value used is as calculated in (c) above