Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | A60 – Matematika Aktuaria |
| Periode Ujian | : | November 2017 |
| Nomor Soal | : | 3 |
SOAL
Untuk suatu model “2-year selection and ultimate mortality”, diberikan :
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 10.140\)
- \({l_{77}} = 9.849\)
Hitunglah
- 10.120
- 10.125
- 10.130
- 10.133
- 10.135
PEMBAHASAN
| Kalkulasi | \({q_{\left[ {75} \right] + 1}} = 0,95{q_{76}}\)
\(1 – {p_{\left[ {75} \right] + 1}} = 0,95(1 – {p_{76}})\)
\(1 – \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}} = 0,95\left( {1 – \frac{{{l_{77}}}}{{{l_{76}}}}} \right)\)
\(1 – \frac{{9.849}}{{{l_{\left[ {75} \right] + 1}}}} = 0,95\left( {1 – \frac{{9.849}}{{10.140}}} \right)\)
\(1 – \frac{{9.849}}{{{l_{\left[ {75} \right] + 1}}}} = \frac{{1.843}}{{67.600}}\)
\(\frac{{9.849}}{{{l_{\left[ {75} \right] + 1}}}} = 0,972737\)
\({l_{\left[ {75} \right] + 1}} = 10.125\) |
| Jawaban | b. 10.125 |
