You are given:

(i) [math]\quad A_{x}=0.30[/math]

(ii) [math]\quad A_{x+n}=0.40[/math]

(iii) [math]A_{x: n} \frac{1}{}=0.35[/math]

(iv) [math]i=0.05[/math]

Calculate [math]a_{x: n}[/math].

• 9.3
• 9.6
• 9.8
• 10.0
• 10.3

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

Answer: B

[math]A_{x: n \mid}^{1}={ }_{n} E_{x}[/math]

[math]A_{x}=A_{x: n}^{1}+{ }_{n} E_{x} A_{x+n}[/math]

[math]0.3=A_{x: n}^{1}+(0.35)(0.4) \Rightarrow A_{x: n}^{1}=0.16[/math]

[math]A_{x: n}=A_{x: n}^{1}+{ }_{n} E_{x}=0.16+0.35=0.51[/math]

[math]\ddot{a}_{x: n}=\frac{1-A_{x: n}}{d}=\frac{1-0.51}{(0.05 / 1.05)}=10.29[/math]

[math]a_{x: n}=\ddot{a}_{x: n}-1+{ }_{n} E_{x}=10.29-0.65=9.64[/math]

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