ACMA 320 Actuarial Mathematics I Assignment 7 Answer Key

i = 0.05, x = 30 n = 15, m = 4

i = 0.06, x = 60 n = 35, m = 12

1. n-year term insurance

(a) E(Z) 0.036517 0.373683 (b) SD(Z) 0.153565 0.238679 (c) 𝑍!.!" 0 0.5217

𝑍!.!" 0 0.7400 (d) 𝑆!.!"!" 2.5582 19.8225

𝑆!.!"!" 3.2174 20.8471 (e) 𝑆!.!"!"## 96.4706 942.258

𝑆!.!"!"## 101.1317 949.5026 2. n-year term

life annuity

(a) E(Y) 10.501861 10.588197 (b) SD(Y) 1.048798 3.852712 (c) 𝑌!.!" 10.7020 13.7385

𝑌!.!" 10.7020 14.8309 (d) 𝑆!.!"!" 530.10 547.78

𝑆!.!"!" 534.60 564.32 (e) 𝑆!.!"!"## 26290.02 26600.42

𝑆!.!"!"## 26321.86 26717.36 3. n-year term

life annuity (Woolhouse)

10.502152 10.588842