Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Untuk suatu model “2-year selection and ultimate mortality”, diberikan:
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 96.815\)
- \({l_{77}} = 96.124\)
Hitunglah \({l_{\left[ {75} \right] + 1}}\)
- 96.150
- 96.780
- 97.420
- 98.050
- 98.690
| Diketahui | Untuk suatu model “2-year selection and ultimate mortality”, diberikan:
|
| Rumus yang digunakan | \({}_t{p_x} = \frac{{{l_{x + t}}}}{{{l_x}}}\) \({}_t{q_x} = \frac{{{l_x} – {l_{x + t}}}}{{{l_x}}}\) |
| Proses pengerjaan | \({p_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\) \(1 – {q_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\) \(1 – 0.95{q_{76}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\) \({l_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{1 – 0.95\left( {\frac{{{l_{76}} – {l_{77}}}}{{{l_{76}}}}} \right)}}\) \({l_{\left[ {75} \right] + 1}} = \frac{{96,124}}{{1 – 0.95\left( {\frac{{96,815 – 96,124}}{{96,815}}} \right)}} = 96,780.21414\) |
| Jawaban | B. 96.780 |