Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2016 |
| Nomor Soal |
: |
26 |
SOAL
Diberikan suatu “survival function”
\({S_0}\left( x \right) = \frac{1}{{1 + \sqrt x }}\)
Hitunglah \({}_{\left. 5 \right|10}{q_{15}}\)
- 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 |
\({}_t{p_x} = \frac{{{S_0}\left( {x + t} \right)}}{{{S_0}\left( x \right)}}\)
\({}_t{p_x} = \frac{{\frac{1}{{1 + \sqrt {x + t} }}}}{{\frac{1}{{1 + \sqrt x }}}}\)
\({}_t{p_x} = \frac{{1 + \sqrt x }}{{1 + \sqrt {x + t} }}\)
\({}_5{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }}\)
\({}_{15}{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {30} }}\)
\({}_{\left. 5 \right|10}{q_{15}} = {}_5{p_{15}} – {}_{15}{p_{15}}\)
\({}_{\left. 5 \right|10}{q_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }} – \frac{{1 + \sqrt {15} }}{{1 + \sqrt {30} }}\)
\({}_{\left. 5 \right|10}{q_{15}} = 0.1381827\) |
| Jawaban |
E. 0,14 |
