Tutorial 4

Tutorial 4 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 4 Feb. 22, 2008 1 Review 1. Continuous Annuity – payments are made continuously, i.e. frequency of payment tends to infinite, or m → ∞ . Present Value a n | i = Z n 0 v t d t = 1 - v n δ = lim m →∞ a ( m ) n | i = lim m →∞ 1 - v n i ( m ) a n | i = i δ a n | i Future Value s n | i = Z n 0 (1 + i ) n - t d t = (1 + i ) n - 1 δ = lim m →∞ s ( m ) n | i s n | i = a n | i (1 + i ) n 2. Varying Annuities (1) Payments varying in AP– payments begin at P and increase by Q per period thereafter. Immediate situation PV I = Pa n | i + Q a n | i - nv n i AV I = PV I (1 + i ) n = Ps n | i + Q s n | i - n i PV I ( ) = P i + Q i 2 Due situation PV D = PV I (1 + i ) AV D = AV I (1 + i ) = PV I (1 + i ) n +1 PV D ( ) = PV I ( )(1 + i ) = P + Q i 1
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(2) Special Cases Immediate situation ( Ia ) n | i = a n | i + a n
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Tutorial 4 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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