Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2015 |
| Nomor Soal | : | 5 |
SOAL
Diketahui dari suatu tabel double-decrement
- \(q_{71}^{\left( 1 \right)} = 0,02\)
- \(q_{71}^{\left( 2 \right)} = 0,06\)
- Setiap decrement berdistribusi seragam (UUD) pada setiap tahun usia dalam tabel double-decrement
Hitunglah \(1.000q_{71}^{‘\left( 1 \right)}\)
- 20,57
- 20,59
- 20,61
- 20,63
- 20,65
| Diketahui | - \(q_{71}^{\left( 1 \right)} = 0,02\)
- \(q_{71}^{\left( 2 \right)} = 0,06\)
- Setiap decrement berdistribusi seragam (UUD) pada setiap tahun usia dalam tabel double-decrement
|
| Rumus yang digunakan | \({}_tp_x^{‘\left( j \right)} = {\left( {{}_tp_x^{\left( \tau \right)}} \right)^{\frac{{q_x^{\left( j \right)}}}{{q_x^{\left( \tau \right)}}}}}\); \({}_tp_x^{\left( \tau \right)} = 1 – {}_tq_x^{\left( \tau \right)} = 1 – \sum\limits_{j = 1}^n {{}_tq_x^{\left( j \right)}} \); \({}_tq_x^{‘\left( j \right)} = 1 – {}_tp_x^{‘\left( j \right)}\) |
| Proses pengerjaan | \(p_{71}^{\left( \tau \right)} = 1 – q_{71}^{\left( \tau \right)} = 1 – q_{71}^{\left( 1 \right)} – q_{71}^{\left( 2 \right)} = 1 – 0.02 – 0.06 = 0.92\) |
| \(p_{71}^{‘\left( 1 \right)} = {\left( {p_{71}^{\left( \tau \right)}} \right)^{\frac{{q_{71}^{\left( j \right)}}}{{q_{71}^{\left( \tau \right)}}}}} = {\left( {0.92} \right)^{\frac{{0.02}}{{0.02 + 0.06}}}} = 0.979370\) |
| \(1000q_{71}^{‘\left( 1 \right)} = 1000\left( {1 – p_{71}^{‘\left( 1 \right)}} \right) = 1000\left( {1 – 0.979370} \right) = 20.63\) |
| Jawaban | d. 20,63 |
