2007_exam_solutions

# 2007_exam_solutions - MA315/07 turn over UNIVERSITY OF KENT...

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Unformatted text preview: MA315/07 turn over UNIVERSITY OF KENT FACULTY OF SCIENCE, TECHNOLOGY AND MEDICAL STUDIES LEVEL C EXAMINATION FINANCIAL MATHEMATICS Tuesday, 22 May 2007: 14.00 – 17.00 This paper contains THIRTEEN 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. MA315/07 2 1 If i = 0.08, calculate to 4 decimal places; (a) 4 5 ( ) a ɺɺ (b) ( ) 10 Ia (c) 9 s (d) 4 3 10 ( ) a (e) ( ) 15 Da ɺɺ (f) 12 4 ( ) s [Total: 10 marks] 2 A man invests £100 with a bank for 10 years. The bank agrees to pay compound interest at a rate of 2% p.a . for the first 2 years, 4% p.a . paid continuously for the next 5 years, 3.5% p.a. convertible quarterly for the next 2 years and then 1% per month for the remainder of the period. How much does the man have at the end of 10 years? [Total: 3 marks] 3 The force of interest is given by; ( ) t δ = 0.04 for 3 t < ≤ ( ) t δ = 0.02 + 0.01 t for 3 10 t < < What is the present value of a payment of £100 at time t = 5 and a payment of £50 at time t = 1. [Total: 5 marks] MA315/07 3 turn over 4 (a) Describe the cashflows involved with the following assets; (i) Fixed Interest Security (ii) Equities [3 marks] (b) The Government is issuing a 5 year fixed interest bond with coupon payments of 4% p.a. payable half yearly in arrears. The bond will be redeemed at par. How much should an investor who pays tax on income and capital gains at a rate of 40% pay for this bond if he wants to achieve a yield of 5% p.a. ? [5 marks] (c) Describe briefly the characteristics of a property investment. [4 marks] [Total: 12 marks] 5 List in order of size the following; (i) 5 5 . % i = (ii) 5 5 . % d = (iii) 4 5 5 ( ) . % i = (iv) 5 5 . % δ = [Total: 3 marks] 6 Miss Jones is buying a new car from her local dealership. She can either pay the purchase price or arrange to pay for the car under a finance package where she will pay an initial deposit of £250, monthly payments in arrears of £203.61 for three years and a final lump sum payment of £3,500 at the end of the 3 years. The APR for this finance package is 11.5%. (a) Calculate the purchase price for the car Miss Jones is buying? [4 marks] (b) If she pays a larger initial deposit of £500, how much does the final lump sum reduce by assuming that the monthly payments and the APR remain unchanged? [2 marks] (c) Assume Miss Jones paid a £500 deposit. Miss Jones decides to sell the car after just 2 years for £6,250. How much money does she make/lose after repaying the outstanding finance plus an early cancellation fee of £150....
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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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2007_exam_solutions - MA315/07 turn over UNIVERSITY OF KENT...

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