Fundamentals of Actuarial Mathematics, 3rd Edition

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) i_r = 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  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.