You are given:

(i) [math]\quad q_{60}=0.01[/math]

(ii) Using [math]i=0.05, A_{60: 31}=0.86545[/math]

Using [math]i=0.045[/math] calculate [math]A_{60: 3}[/math].

• 0.866
• 0.870
• 0.874
• 0.878
• 0.882

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

Answer: D

[math]A_{60: 31}=q_{60} v+\left(1-q_{60}\right) q_{60+1} v^{2}+\left(1-q_{60}\right)\left(1-q_{60+1}\right) v^{3}=0.86545[/math]

[math]q_{60+1}=\frac{A_{60: 31}-q_{60} v-\left(1-q_{60}\right) v^{3}}{\left(1-q_{60}\right) v^{2}-\left(1-q_{60}\right) v^{3}}=\frac{0.86545-\frac{0.01}{1.05}-\frac{0.99}{1.05^{3}}}{\frac{0.99}{1.05^{2}}-\frac{0.99}{1.05^{3}}}=0.017[/math] when [math]v=1 / 1.05[/math].

The primes indicate calculations at [math]4.5 \%[/math] interest.

[[math]] \begin{aligned} A_{60: 3}^{\prime} & =q_{60} v^{\prime}+\left(1-q_{60}\right) q_{60+1} v^{\prime 2}+\left(1-q_{60}\right)\left(1-q_{60+1}\right) v^{\prime 3} \\ & =\frac{0.01}{1.045}+\frac{0.99(0.017)}{1.045^{2}}+\frac{0.99(0.983)}{1.045^{3}} \\ & =0.87777 \end{aligned} [[/math]]

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