Pembahasan Soal Ujian Profesi Aktuaris
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 |