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W09Final - University of Waterloo Final Examination Term...

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University of Waterloo Final Examination Term: Winter Year: 2009 First (Given) Name: Last (Family) Name: Student ID #: userid: Course Abbreviation and Number: ACTSC 231 Course Title: Mathematics of Finance Section(s): 001 Sections Combined Course(s): N/A Section Numbers of Combined Course(s): N/A Instructor: Diana Chisholm Date of Exam: April 23, 2009 Time Period: Start time: 4:00 pm End Time: 6:30 pm Duration of Exam: 2.5 hours Number of Exam Pages: 9 (including this cover sheet and tables) Exam Type: Special Materials Additional Materials Allowed: Calculator Marking Scheme: Question Marks available Marks obtained 1 8 2 8 3 14 4 10 5 7 6 10 7 13 8 10 Total 80
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ACTSC 231, April 23/09, 4:00-6:30pm Page 2 of 9 1. [8 marks] The accumulation function of an account is a ( t ) = αt 2 + βt + 1, where α and β > 0 . (a) [2 marks] Derive an expression for the force of interest at time t , δ t . (b) [2 marks] Is δ t an increasing, decreasing, or constant function of t ? What does that tell you about how fast money grows in this account as compared to a compound interest account? (c) [4 marks] If the effective rate of interest over the second year, i 2 is 9.4340% and the effective rate of discount over the first year, d 1 is 5.6604%, find α and β . (Hint: first find α + β .)
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ACTSC 231, April 23/09, 4:00-6:30pm Page 3 of 9 2. [8 marks] The UW pension plan fund had a value of $24,500 on Jan 1, 2006. On May 1, 2008, the balance was $28,212 and $10,000 was withdrawn. On Dec 1, 2008, the balance was $15,892 and $8,000 was deposited. On Jan 1, 2009, the balance was $30,309. Assume each month is 1/12 of a
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