Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
Mei 2018 |
| Nomor Soal |
: |
6 |
SOAL
Jika \({l_x} = 140\) dan \({q_x} = \frac{1}{5}.{\rm{ }}\) Hitunglah \({l_{x + 1/4}}\) menggunakan asumsi Hyperbolic (Balduci)
- 129
- 130
- 131
- 132
- 133
| Diketahui |
\({l_x} = 140\) dan
\({q_x} = \frac{1}{5}\) |
| Rumus yang digunakan |
Dalam asumsi hyperbolic dipunyai
\({l_{x + s}} = \frac{{{l_{x + 1}}}}{{{p_x} + s{q_x}}}\)
\(_s{q_x} = \frac{{s{q_x}}}{{1 – (1 – s){q_x}}}\) |
| Proses pengerjaan |
\({p_x} = 1 – {q_x} = 1 – \frac{1}{5} = \frac{4}{5} = 0.8\)
\({p_x} = \frac{{{l_{x + 1}}}}{{{l_x}}} \Leftrightarrow = {l_{x + 1}} = {l_x}{p_x} = (0.8)(140) = 112\)
\({l_{x + 1/4}} = {l_{x + 0.25}} = \frac{{{l_{x + 1}}}}{{{p_x} + 0.25{q_x}}} = \frac{{112}}{{0.8 + (0.25)(0.2)}} = \frac{{112}}{{0.85}} = 131.76 = 132\) |
| Jawaban |
d. 132 |
