Solve the following questions appropriately. Ensure precision in your working.

A life table with a select period of 2 years is based on rates of mortality, which satisfy the following relationship: 1 Xqx (for all values of x , and r = 0,1) 960 = 0.0195 , 461 = 0.0198, 962 = 0.0200 and /63 = 100,000 (i) Calculate: (a) 62 (b) 4601+1 (c) 4160] [4] (ii) A select life aged 60 subject to the mortality table described in (i) above purchases a 3-year endowment assurance with sum assured $10,000. Premiums of f3,000 are payable annually throughout the term of the policy or until earlier death. The death benefit is payable at the end of the year of death. Calculate the expected value of the present value of the profit or loss to the office on the contract, assuming an effective rate of interest of 6% pa, and ignoring expenses. [4] [Total 8]Trevor and Simone have taken early retirement. Their retirement package has left each of them with a lump sum that is substantial, but they have decided to start a business together in the hope of accumulating significant wealth before reaching normal retirement age in eight to ten years. They have identified an opportunity to import consumer electronics from the Far East. They have established that there is a substantial niche market in the UK for products such as mobile phones and tablet computers that are produced for the Chinese market and which are rarely exported. Trevor and Simone have negotiated the exclusive UK rights to import a new line of products that is presently in the final development stage. They have a few months to establish their company and to ensure that all of their distribution lines are in place. Their retirement payments will only provide approximately 60% of their funding requirements. They are unsure whether to raise additional funds by inviting investors to become minority shareholders in this venture, or to seek a bank loan, or a combination of the two. (1) Discuss the relative merits of the bank loan or additional equity from minority shareholders for Trevor and Simone's company. [10] (ii) Discuss the difficulties associated with determining the optimal gearing level for Trevor and Simone's company. [10] [Total 20]