Finance > EXAM > FINAL EXAM FOR AS1201 Financial & Investment Mathematics [CT1]...SUMMER 2019 (All)

FINAL EXAM FOR AS1201 Financial & Investment Mathematics [CT1]...SUMMER 2019

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Part of Subject CT1 of the Institute and Faculty of Actuaries Examinations Part 1 Examination 26th May 2020 10:00 – 13:00 Instructions to students: Candidates should answer ALL NINE questions. ... The number of marks allocated is shown at the end of each question. Where marks have been quoted for parts of questions, these are intended to be a helpful guide to the candidates. This examination paper consists of 7 printed pages including the title page. Materials: Number of answer books to be provided: 1 Only the Casio calculators FX-83 (MS, ES or GT+) or FX-85 (MS, ES or GT+) are permitted for use in this exam. Dictionaries are not permitted. Actuarial Tables. This examination paper may be removed from the examination room. External Examiner: Mr Niall Franklin Internal Examiner: Professor Ben Rickayzen BSc (Hons) Degree in Actuarial Science Page 2 of 7 Question 1 A pension fund purchased a fixed-interest bond with exactly 15 years to redemption. The bond pays coupons of 5% per annum quarterly in arrears and is redeemable at 105. (i) Assuming that the gross redemption yield at the date of purchase was 7% per annum effective and that the pension fund does not pay tax on income and capital gains, calculate the purchase price of the bond per £100 nominal. [3 marks] (ii) Eight years later, immediately after the payment of the coupon then due, the pension fund sold the bond to an individual investor who pays tax at a rate of 27% on income and 20% on capital gains. Assuming that the bond was purchased by the individual investor to give a net redemption yield of 6% per annum, calculate the price per £100 nominal at which the pension fund sold the bond. [5 marks] [Total 8 marks] Question 2 In any year, the rate of interest on funds invested with a given insurance company is independent of the rates of interest in all previous years. Each year the value of 1 ,  it  where it is the rate of interest earned in the tth year, is lognormally distributed. The mean and standard deviation of it are 0.06 and 0.17 respectively. (i) Determine the parameters  and  2 of the lognormal distribution of 1it . [5 marks] (ii) (a) Determine the distribution of S20, where S20 denotes the accumulation of one unit of money over 20 years. (b) Calculate the probability that S20  4.5. [4 marks] [Total 9 marks] [Show More]

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