Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2015 |
| Nomor Soal | : | 6 |
SOAL
Untuk suatu model “2-year selection and ultimate mortality”, diketahui:
- \({q_{\left[ x \right] + 1}} = 0,96{q_{x + 1}}\)
- \({l_{76}} = 76.213\)
- \({l_{77}} = 75.880\)
Hitunglah \({l_{\left[ {75} \right] + 1}}\)
- 75.900
- 76.000
- 76.100
- 76.200
- 76.300
| Diketahui | Suatu model “2-year selection and ultimate mortality”, diketahui:- \({q_{\left[ x \right] + 1}} = 0,96{q_{x + 1}}\)
- \({l_{76}} = 76.213\)
- \({l_{77}} = 75.880\)
|
| Rumus yang yang digunakan | \({q_x} = 1 – {p_x} = 1 – \frac{{{l_{x + 1}}}}{{{l_x}}}\) dan \({p_{\left[ x \right] + 1}} = \frac{{{l_{x + 2}}}}{{{l_{\left[ x \right] + 1}}}}\) |
| Proses pengerjaan | \({q_{76}} = 1 – \frac{{{l_{77}}}}{{{l_{76}}}} = 1 – \frac{{75,880}}{{76,213}} = 0.004369\) |
| \({q_{\left[ {75} \right] + 1}} = 0.95{q_{76}} = 0.95\left( {0.004369} \right) = 0.004151\) |
| \({l_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{p_{\left[ {75} \right] + 1}}}} = \frac{{75,880}}{{1 – 0.004151}} = 76,196\) |
| Jawaban | d. 76.200 |
