Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
Juni 2015 |
| Nomor Soal |
: |
20 |
SOAL
Diberikan suatu kematian mengikuti \({l_x} = 100 – x\); \(0 \le x \le 100\)
Hitunglah \({e_{85,2}}\) (gunakan pembulatan terdekat)
- 6.890
- 6.895
- 6.900
- 6.905
- 6.910
| Diketahui |
\({l_x} = 100 – x\); \(0 \le x \le 100\) |
| Rumus yang digunakan |
\({}_t{p_x} = \frac{{{l_{x + t}}}}{{{l_x}}}\)
\({e_x} = \sum\limits_{k = 1}^\infty {{}_k{p_x}} \)
\(\sum\limits_{k = 1}^n k = \frac{{n\left( {n + 1} \right)}}{2}\) |
| Proses Pengerjaan |
\({e_{85.2}} = \sum\limits_{k = 1}^{14} {{}_k{p_{85.2}}} = \sum\limits_{k = 1}^\infty {\frac{{{l_{85.2 + k}}}}{{{l_{85.2}}}}} \)
\({e_{85.2}} = \sum\limits_{k = 1}^{14} {\frac{{100 – 85.2 – k}}{{100 – 85.2}}} \)
\({e_{85.2}} = \sum\limits_{k = 1}^{14} {\frac{{14.8}}{{14.8}}} – \sum\limits_{k = 1}^{14} {\frac{k}{{14.8}}} \)
\({e_{85.2}} = 14 – \frac{{\frac{{\left( {14} \right)\left( {15} \right)}}{2}}}{{14.8}}\)
\({e_{85.2}} = 6.90541\) |
| Jawaban |
d. 6.905 |
