Given the questions below answer them well.thanks

1 (i) In a combined sickness and mortality table Ki+1 = 554, 405 2x = 1.129 Dx = 24, 510 Drti = 23, 425 Estimate KI- (ii) An office offers an optional waiver of premium benefit on sickness of any duration in respect of a 25-year with or without profits endowment assurance policy with weekly premiums payable for 25 years or until earlier death. There is a waiting period of 12 months for the waiver of premium benefit, and, during the second year of the policy, only half the premium (including the extra premium for the waiver benefit) is waived. The sum assured under the endowment policy is payable immediately on death, or on survival until the end of the term. Using the basis given below, calculate the percentage by which the normal weekly premium (i.e. the premium for a policy without the waiver benefit) for a life aged exactly 30 at entry should be increased in order to provide the waiver benefit. mortality: English Life Table No.12-Males; sickness: Manchester Unity 1893-97, Occupation Group AH.J; interest: 4% per annum; expenses: 15% of each extra premium for the waiver benefit. .2 A policy issued by a life office to a male life aged exactly 35 is subject to level weekly premiums ceasing at exact age 65. If the man has been sick for 6 months or more when a premium falls due, the premium is waived. The policy provides the following benefits: (a) on survival to exact age 65, an annuity of 25,000 per annum payable monthly in advance, (b) on death before age 65, a return of all premiums paid (including those waived during sickness) together with compound interest at 4% per annum to the date of death. There is no waiting period and the off periods are the same as those underlying the tables in Formulae and Tables for Actuarial Examinations. Calculate the weekly premium. Basis: English Life Table No.12-Males, Manchester Unity Sickness Experience 1893-97, Oc- cupation Group AHJ, interest 4% per annum, no expenses. 3 (a) Ten years ago, a man then aged exactly 30 effected an insurance policy providing sickness benefits of f100 per week for the first six months of sickness, 250 per week for the remainder of the first year and f30 per week thereafter, with benefit ceasing at age 60. Calculate the weekly premium payable to age 50 on the following basis: Mortality: English Life Table No. 12 - Males; Sickness: Manchester Unity 1893-97, Occupation Group AHJ; Interest: 4% per annum; Expenses: 10% of each premium. (b) The man now wishes to alter his policy so that premiums will in future be waived during all periods of sickness. Calculate the revised premium payable assuming that the alteration basis follows the premium basis above. Note. Expenses are incurred even when premiums are waived.A certain friendly society recruits only married men aged under 55. The society provides the following benefits: (i) immediately on the death of the member at any age, f2,000, (ii) during the first 10 years of membership, immediately on the death of the member's wife before her husband, f500, (iii) on survival of the member to age 65, an annuity of f10 per week for life, and (iv) during any spell of sickness of the member before age 65, f10 per week reducing to f6 per week after 3 months' sickness. The basis for all calculations is: mortality of members: E.L.T. No. 12 - Males mortality of wives: E.L.T. No. 12 - Males with an age-deduction of 5 years interest: 4% per annum sickness: Manchester Unity 1893-97 AHJ expenses: 5% of all contributions, including those waived during sickness Wives of members are taken as being of the same age as their husbands; there is no benefit on the death of wives of marriages taking place after entry to the society, and the possibility of divorce is to be ignored. There is no waiting period and the off-period is as in the Tables provided. The possibility of withdrawal is ignored. (a) Calculate the weekly contribution rate, waived during sickness and ceasing at age 65 or the previous death of the member, for an entrant aged 25. (b) Calculate the reserve for a member aged 35 who joined at age 25. Note Use Simpson's rule for approximate integration, i.e. [ f(t) at =6 b - " [ f ( a ) + of ( ", ) + f (b ) ] A Friendly Society issues policies providing the following benefits: (i) A sickness benefit of f25 per week for the first 13 weeks of sickness and f12.50 per week thereafter, benefit ceasing at age 60. Contributions are waived during sickness. (ii) On death before age 60, a lump sum of f1,000 plus a return of contributions (including any waived) without interest. (iii) On survival to age 60, a lump sum of f2,000. Contributions are payable by level weekly amounts until age 60. There is a six-month waiting period for the sickness benefit (including the premium waiver) and the off-period may be assumed to be the same as that underlying the tables in "Formulae and Tables for Actuarial Examinations" . (a) Calculate the weekly contribution payable by a new member aged 35 on the basis given below. (b) Calculate the reserve (on the basis given below) to be held for this member five years after he joins the Society. Basis: English Life Table No. 12 - Males Manchester Unity Sickness Experience 1893-97, Occupation Group AH.J interest 4% per annum. expenses are 5% of all premiums (including those waived).6 A friendly society provides the following benefits: (i) On sickness, f40 per week for the first 26 weeks and f50 per week for the next 26 weeks. No sickness benefit is payable after age 65. (ii) On attaining age 65 or immediately on earlier death, the sum of 23,000. Members contribute f1 per week, ceasing at age 65 or earlier death, but this is waived during periods of sickness (whether benefit is payable or not.) Calculate the reserve which should be held for a member aged 50, using the following basis: English Life Table No. 12 - Males, 4 per annum interest, Manchester Unity Sickness Experience 1893-97 (AHJ). There is no waiting period, and off-periods are as in "Formulae and Tables for Actuarial Examinations" . 7 On 1 January 1995 a friendly society had in force a large group of policies providing certain sickness and life assurance benefits. These policies had all been issued 10 years ago to lives now aged 45. The benefits cease when the policyholders reach age 65, and the policies have level weekly premiums payable throughout the term of the policy. Each policy provides an income of f20 per week during any period of sickness which has lasted more than 6 months. and a lump sum of f20,000 immediately on death before age 65. Premiums are waived during sickness (even when no benefit is payable), and the off-period is as in the Manchester Unity sickness tables. The basis for the calculation of premiums and reserves is: Mortality: E.L.T. 12 - Males Interest: 4% p.a. Sickness: Manchester Unity Experience 1893-97 (Occupation Group AHJ) Expenses: 20% of all premiums, including those waived (a) Calculate the weekly premium for each of these policies. (b) Calculate the reserve per policy in force on 1 January 1995