2008_exam_solutions

2008_exam_solutions - MA315/08 turn over UNIVERSITY OF KENT...

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Unformatted text preview: MA315/08 turn over UNIVERSITY OF KENT FACULTY OF SCIENCE, TECHNOLOGY AND MEDICAL STUDIES LEVEL C EXAMINATION FINANCIAL MATHEMATICS Thursday, 29 May 2008: 9.30 – 12.30 This paper contains TWELVE questions. Answer ALL questions. The marks allocated are shown at the end of each question. Candidates are advised to show their working on their scripts. Marks might then be awarded for use of a correct method, even if the numerical or algebraic result is incorrect . Copies of Formulae and Tables for Actuarial Examinations are provided. Approved calculators may be used. MA315/08 2 1 (i) Calculate the present value on 1 January of £40 paid on 30 June and 31 December each year for 5 years using an interest rate of i = 5% per annum. (ii) Calculate the accumulated value at the end of 8 years of £100 paid at the end of year 1, £120 at the end of year 2 and so on until £240 paid at the end of year 8. Use a nominal interest rate of 10% per annum convertible half yearly. (iii) Calculate the present value of £200 paid each year continuously for 3 years using an interest rate of 2% per annum. (iv) Calculate the present value of £10 a year paid quarterly in advance for 10 years using a force of interest of 5% per annum. [Total: 7 marks] 2 You are given the following information; 0 9 0 01 ( ) . . v t t =- where ( ) v t is the present value factor applicable at time t (a) Calculate the accumulated value at the end of 5 years of £100 paid at the beginning of the first year. [2 marks] (b) Calculate the value at the end of the 4 th year of £200 paid at time after 7 years. [2 marks] (c) Calculate the accumulated value at the end of 6 years of £150 received at the end of 2 years. [2 marks] [Total: 6 marks] MA315/08 3 turn over 3 The force of interest is given by the following function; ( ) 0 07 0 005 . . t t δ = + 3 t ≤ < ( ) 0 085 . t δ = 3 6 t ≤ < ( ) 0 085 0 01 . . t t δ =- 6 t ≥ (a) Calculate the combined present value of £100 paid at time t = 2 and £500 paid at time t = 7. [5 marks] (b) Calculate the equivalent annual effective interest rate achieved over the first 6 years. [2 marks] (c) Calculate the accumulated value at time t = 6 of £100 each year paid continuously for time 3 to time 6. [3 marks] [Total: 10 marks] 4 Mr Smith has £5,000 and he is looking to invest in Company ABC. Company ABC has shares which are expected to provide regular dividends annually. The next dividend is expected to be £4.50 and will be paid in 2 months time. Dividends are expected to increase by 2% per annum. (a) Describe the characteristics of equities. [3 marks] (b) Shares can only be purchased in blocks of 10. How many shares can Mr Smith buy with his £5,000? Use an effective interest rate of 6% per annum....
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This note was uploaded on 06/07/2011 for the course MA 826 taught by Professor Loba,millet during the Spring '11 term at Kent Uni..

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2008_exam_solutions - MA315/08 turn over UNIVERSITY OF KENT...

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