You are given the following survival function of a newborn:

[[math]] S_{0}(x)= \begin{cases}1-\frac{x}{250}, & 0 \leq x\lt40 \\ 1-\left(\frac{x}{100}\right)^{2}, & 40 \leq x \leq 100\end{cases} [[/math]]

Calculate the probability that (30) dies within the next 20 years.

• 0.13
• 0.15
• 0.17
• 0.19
• 0.21

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: B

[[math]] \begin{aligned} & { }_{20} q_{30}=\frac{S_{0}(30)-S_{0}(50)}{S_{0}(30)}=\frac{\left(1-\frac{30}{250}\right)-\left(1-\left[\frac{50}{100}\right]^{2}\right)}{1-\frac{30}{250}}=\frac{\frac{220}{250}-\frac{3}{4}}{\frac{220}{250}} \\ & =\frac{440-375}{440}=\frac{65}{440}=\frac{13}{88}=0.1477 \end{aligned} [[/math]]

Copyright 2024 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.