Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Startistika |
| Periode Ujian | : | Juni 2016 |
| Nomor Soal | : | 6 |
SOAL
Dalam table mortalita select dan ultimate 2 tahun, Anda diberikan informasi sebagai berikut:
\({q_{\left[ x \right] + 1}} = 0,92{q_{x + 1}}\)
\({l_{58}} = 85.681\)
\({l_{59}} = 83.546\)
Hitunglah \({l_{\left[ {57} \right] + 1}}\) (dibulatkan)
- 80.436
- 80.952
- 81.772
- 82.315
- 85.506
| Diketahui | \({q_{\left[ x \right] + 1}} = 0,92{q_{x + 1}}\)
\({l_{58}} = 85.681\)
\({l_{59}} = 83.546\) |
| Rumus yang digunakan | \({q_x} = \frac{{{l_x} – {l_{x + 1}}}}{{{l_x}}}\)
\({q_{\left[ x \right] + 1}} = \frac{{{l_{\left[ x \right] + 1}} – {l_{x + 2}}}}{{{l_{\left[ x \right] + 1}}}}\) |
| Proses pengerjaan | \({q_{58}} = \frac{{{l_{58}} – {l_{59}}}}{{{l_{58}}}}\)
\(= \frac{{85.681 – 83.546}}{{85.681}}\)
\(= 0,024918\) |
| \({q_{\left[ {57} \right] + 1}} = 0,92{q_{58}}\)
\(= 0,92 \cdot 0,024918\)
\(= 0,022925\) |
| \({q_{\left[ {57} \right] + 1}} = \frac{{{l_{\left[ {57} \right] + 1}} – {l_{59}}}}{{{l_{\left[ {57} \right] + 1}}}}\)
\(0,022925 = \frac{{{l_{\left[ {57} \right] + 1}} – 83.546}}{{{l_{\left[ {57} \right] + 1}}}}\)
\({l_{\left[ {57} \right] + 1}} – 0,022925 \cdot {l_{\left[ {57} \right] + 1}} = 83.546\)
\({l_{\left[ {57} \right] + 1}} = \frac{{83.546}}{{0,977075}}\)
\(= 85.506,23\) |
| Jawaban | e. 85.506 |
