Tutorial 3

Tutorial 3 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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Unformatted text preview: 07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 3 1 Review 1.1 Basic Formulas 1. Annuity-immediate & Annuity-due ( a n e i = v + v 2 + ··· + v n = 1- v n i s n e i = 1 + (1 + i ) + (1 + i ) 2 + ··· + (1 + i ) n- 1 = (1+ i ) n- 1 i ( ¨ a n e i = 1 + v + v 2 + ··· + v n- 1 = 1- v n d ¨ s n e i = (1 + i ) + (1 + i ) 2 + ··· + (1 + i ) n = (1+ i ) n- 1 d ( a ( m ) n e i = 1 m [ v 1 m + v 2 m + ··· + v n ] = 1- v n i ( m ) s ( m ) n e i = 1 m [1 + (1 + i ) 1 m + (1 + i ) 2 m + ··· + (1 + i ) n- 1 m ] = (1+ i ) n- 1 i ( m ) ( ¨ a ( m ) n e i = 1 m [1 + v 1 m + v 2 m + ··· + v n- 1 m ] = 1- v n d ( m ) ¨ s ( m ) n e i = 1 m [(1 + i ) 1 m + (1 + i ) 2 m + ··· + (1 + i ) n ] = (1+ i ) n- 1 d ( m ) 2. Perpetuities ( a ∞e i = lim n →∞ 1- v n i = 1 i ¨ a ∞e i = lim n →∞ 1- v n d = 1 d 1.2 Other Formulas ( ¨ a n e i = a n e i (1 + i ) ¨ a ( m ) n e i = a ( m ) n e i (1 + i...
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Tutorial 3 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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