18. For a special fully discrete whole life insurance on (40), you are given:
(i) The death benefit is 1000 during the first 11 years and 5000 thereafter.
(ii) Expenses, payable at the beginning of the year, are 100 in year 1 and 10 in
years 2 and later.
(iii) π is the level annual premium, determined using the equivalence
principle.
(iv) G = 1.02 ×π is the level annual gross premium.
(v) Mortality follows the Illustrative Life Table.
(vi) i = 0.06
(vii) 11 40 E = 0.50330
Calculate the gross premium reserve at the end of year 1 for this insurance.