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Exercise


Jan 16'24

Answer

Answer: C

The number of left-handed members at the end of each year [math]k[/math] is:

[math]L_{0}=75[/math] and [math]L_{1}=(75)(0.75)[/math]

Thereafter, [math]L_{k}=L_{k-1} \times 0.75+35 \times 0.75=75 \times 0.75^{k}+35 \times\left(0.75+0.75^{2}+\ldots 0.75^{k-1}\right)[/math]

Similarly, the number of right-handed members after each year [math]k[/math] is:

[math]R_{0}=25[/math] and [math]R_{1}=(25)(0.5)[/math]

Thereafter, [math]R_{k}=R_{k-1} \times 0.50+15 \times 0.50=25 \times 0.50^{k}+15 \times\left(0.50+0.50^{2}+\ldots 0.50^{k-1}\right)[/math]

At the end of year 5, the number of left-handed members is expected to be 89.5752, and the number of right-handed members is expected to be 14.8435 .

The proportion of left-handed members at the end of year 5 is therefore

[math]\frac{89.5752}{89.5752+14.8438}=0.8578[/math]

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

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