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Fundamentals of Actuarial Mathematics, 3rd Edition by S. David Promislow

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Answers to exercises

Chapter 2

  • 2.1 (a) 6   (b) 150
  • 2.2 1
  • 2.3 4.1
  • 2.4 (a) (1, 2/3, 4/9, 8/27, 2/9, 1/6)   (b)    (c)
  • 2.5 (a) 1.5   (b) 10.75
  • 2.6 (a) − 19/12   (b) 40/3
  • 2.7 (a) 360   (b) 440
  • 2.8 For last part, 17 = 4.4 + 0.7 × 18
  • 2.11 The first.
  • 2.14 d7 = 12.2
  • 2.15 0.8
  • 2.16 (a) 9980.89   (b) 10 117.40
  • 2.17 (a) better off by 133.72   (b) worse off by 61.38
  • 2.28 v(0, 1) = 0.7, v(1, 2) = 0.4375.
  • 2.20 (b) ir = 2r/(1 + r)
  • 2.23 746.92
  • 2.24 0.045
  • 2.25 Initial payment is 8177.15. As examples, outstanding balance at time 5 is 49 560.15, and at time 15 is 19 132.59.

Chapter 3

  • 3.1  
    1. 1000, 800, 600, 450, 315, 189.
    2. (i) 285/800   (ii) 189/600
    3. 2.5052, 2.1315, 1.842, 1.456, 1.08
  • 3.2 0.288
  • 3.3 1/10, 1/6, 4/15, 11/20
  • 3.4 (a) 1 − n/(100 − x)   (b) n/(100 − x)   (c) k/(100 − x), for suitable n, k
  • 3.5 22.8
  • 3.7 (a) (1 − q)n   (b) (1 − q)/q
  • 3.9 e0 = 79.83 for original table. New values are 77.72, 78.41.

Chapter 4

  • 4.1 3.64
  • 4.2 3316.62
  • 4.3 (a) 609.01   (b) 755.95
  • 4.4 16.2
  • 4.5 11 111
  • 4.6 y50 inline 2(2) = 0.384,   y52(2) = 0.48
  • 4.7 1/(1 − v(1 − q))
  • 4.9 19 900
  • 4.10 3.29
  • 4.11 153.85
  • 4.13 947.83
  • 4.14 274 754
  • 4.15 (a) 20   (b) 13
  • 4.16 which is lower since is covers more of the high interest years.

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