Answer all questions below

Question 1.1

Example 18.2.2. A friendly society issued a policy providing the following benefits to a man aged exactly 25 at entry: (a) on death at any time before age 60, the sum of 4,000 payable immediately; (b) on survival to age 60, an annuity of f8 per week payable weekly in advance for as long as he survives; (c) on sickness, an income benefit to be payable during sickness of 232 per week for the first 6 months reducing to f16 per week for the next 18 months and to f8 per week thereafter. Sicknessbenefit is not payable after age 60. There is no waiting period. Premiums are payable monthly in advance for at most 35 years, and are not waived during periods of sickness. The society uses the following basis to calculate premiums. Find the monthly premium. mortality: English Life Table No.12 - Males sickness: Manchester Unity Sickness Experience 1893-97, Occupation Group AH.J interest: 4% p.a. expenses: noneExample 18.3.1. A friendly society issues sickness insurance policies which provide income during periods of sickness as follows: (a) f100 per week while a sickness has duration in excess of 13 weeks but less than 1 year; (b) 275 per week while a sickness has duration in excess of 1 year but less than 2 years; (c) 250 per week while a sickness has duration in excess of 2 years. All benefits cease at age 65. Premiums are payable weekly until age 65 and are waived when sickness benefit is being paid. There is no waiting period. Calculate the weekly premium for a life aged 38 at entry. Basis: mortality: E.L.T. No.12 (Males) sickness: Manchester Unity Sickness Experience 1893-97, Occupation Group AHJ. interest: 4% p.a. expenses: 50% of all premiums payable in the first year, plus 10% of all premiums payable after the first year.1 (i) In a combined sickness and mortality table Kr+1 = 554, 405 2x = 1.129 Dr = 24, 510 Dr+1 = 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 AHJ; 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, $50 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