Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Untuk suatu model “2- year selection and ultimate mortality”, diberikan :
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 98.153\)
- \({l_{77}} = 96.124\)
Hitunglah \({l_{\left[ {75} \right] + 1}}\) (pembulatan terdekat )
- 96.150
- 96.780
- 97.420
- 98.050
- 98.690
| Step | \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\) \(1 – {p_{\left[ x \right] + 1}} = 0,95(1 – {p_{x + 1}})\) \(1 – \frac{{{l_{x + 2}}}}{{{l_{\left[ x \right] + 1}}}} = 0,95\left( {1 – \frac{{{l_{x + 2}}}}{{{l_{x + 1}}}}} \right)\) \(1 – \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}} = 0,95\left( {1 – \frac{{{l_{77}}}}{{{l_{76}}}}} \right)\) \(1 – \frac{{96.124}}{{{l_{\left[ {75} \right] + 1}}}} = 0,95\left( {1 – \frac{{96.124}}{{98.153}}} \right)\) \(1 – \frac{{96.124}}{{{l_{\left[ {75} \right] + 1}}}} = 0,019638\) \(0,980362{l_{\left[ {75} \right] + 1}} = 96.124\) \({l_{\left[ {75} \right] + 1}} = 98.049,496\) \({l_{\left[ {75} \right] + 1}} \cong 98.050\) |
| Jawaban | d. \(98.050\) |