Exercise
A fund is established for the benefit of 400 workers all age 60 with independent future lifetimes. When they reach age 85 , the fund will be dissolved and distributed to the survivors.
The fund will earn interest at a rate of [math]5 \%[/math] per year.
The initial fund balance, [math]F[/math], is determined so that the probability that the fund will pay at least 5000 to each survivor is [math]86 \%[/math], using the normal approximation.
Mortality follows the Standard Ultimate Life Table.
Calculate [math]F[/math].
- 350,000
- 360,000
- 370,000
- 380,000
- 390,000
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: E
Out of 400 lives initially, we expect [math]400_{25} p_{60}=400 \frac{l_{85}}{l_{60}}=400\left(\frac{61,184.9}{96,634.1}\right)=253.26[/math] survivors
The standard deviation of the number of survivors is [math]\sqrt{400_{25} p_{60}\left(1-{ }_{25} p_{60}\right)}=9.639[/math]
To ensure [math]86 \%[/math] funding, using the normal distribution table, we plan for [math]253.26+1.08(9.639)=263.67[/math]
The initial fund must therefore be [math]F=(264)(5000)\left(\frac{1}{1.05}\right)^{25}=389,800[/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.