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 |