Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan suatu “survival function”
\({S_0}\left( x \right) = \frac{1}{{1 + \sqrt x }}\)
Hitunglah \({}_{\left. 5 \right|5}{q_{15}}\)
- 0,06
- 0,08
- 0,10
- 0,12
- 0,14
| Diketahui | \({S_0}\left( x \right) = \frac{1}{{1 + \sqrt x }}\) |
| Rumus yang digunakan | \({}_{\left. t \right|u}{q_x} = {}_t{p_x} – {}_{t + u}{p_x}\) \({}_t{p_x} = {S_x}\left( t \right) = \frac{{{S_0}\left( {x + t} \right)}}{{{S_0}\left( x \right)}}\) |
| Proses pengerjaan | \({}_t{p_x} = \frac{{{S_0}\left( {x + t} \right)}}{{{S_0}\left( x \right)}}\) \({}_t{p_x} = \frac{{\frac{1}{{1 + \sqrt {x + t} }}}}{{\frac{1}{{1 + \sqrt x }}}}\) \({}_t{p_x} = \frac{{1 + \sqrt x }}{{1 + \sqrt {x + t} }}\) \({}_5{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }}\) \({}_{10}{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {25} }}\) \({}_{\left. 5 \right|5}{q_{15}} = {}_5{p_{15}} – {}_{10}{p_{15}}\) \({}_{\left. 5 \right|5}{q_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }} – \frac{{1 + \sqrt {15} }}{{1 + \sqrt {25} }}\) \({}_{\left. 5 \right|5}{q_{15}} = 0.078345\) |
| Jawaban | B. 0,08 |