Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2015 |
| Nomor Soal |
: |
4 |
SOAL
Diberikan sebagai berikut:
- \({l_{\left[ {45} \right]}} = 1000\)
- \({}_5{q_{\left[ {45} \right]}} = 0,04\)
- \({}_5{q_{\left[ {45} \right] + 5}} = 0,05\)
Hitunglah \({l_{\left[ {45} \right] + 10}}\)
- 912
- 960
- 950
- 800
- 990
| Diketahui |
- \({l_{\left[ {45} \right]}} = 1000\)
- \({}_5{q_{\left[ {45} \right]}} = 0,04\)
- \({}_5{q_{\left[ {45} \right] + 5}} = 0,05\)
|
| Rumus yang digunakan |
\({}_u{q_{\left[ x \right] + t}} = 1 – \frac{{{l_{\left[ x \right] + t + u}}}}{{{l_{\left[ x \right] + t}}}}\) |
| Proses pengerjaan |
\({}_5{q_{\left[ {45} \right]}} = 1 – \frac{{{l_{\left[ {45} \right] + 5}}}}{{{l_{\left[ {45} \right]}}}}\)
\({l_{\left[ {45} \right] + 5}} = \left( {1 – {}_5{q_{\left[ {45} \right]}}} \right)\left( {{l_{\left[ {45} \right]}}} \right)\)
\({l_{\left[ {45} \right] + 5}} = \left( {1 – 0.04} \right)\left( {1000} \right) = 960\) |
|
\({}_5{q_{\left[ {45} \right] + 5}} = 1 – \frac{{{l_{\left[ {45} \right] + 10}}}}{{{l_{\left[ {45} \right] + 5}}}}\)
\({l_{\left[ {45} \right] + 10}} = \left( {1 – {}_5{q_{\left[ {45} \right] + 5}}} \right)\left( {{l_{\left[ {45} \right] + 5}}} \right)\)
\({l_{\left[ {45} \right] + 10}} = \left( {1 – 0.05} \right)\left( {960} \right) = 912\) |
| Jawaban |
a. 912 |
