Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
Mei 2018 |
| Nomor Soal |
: |
29 |
SOAL
Berikut adalah select and ultimate life table dengan periode seleksi 3 tahun:
| \(\left[ x \right]\) |
\({l_{\left[ x \right]}}\) |
\({l_{\left[ x \right] + 1}}\) |
\({l_{\left[ x \right] + 2}}\) |
\({l_{\left[ x \right] + 3}}\) |
\(x + 3\) |
| 55 |
10.000 |
9.493 |
8.533 |
7.664 |
58 |
| 56 |
8.547 |
8.028 |
6.889 |
5.630 |
59 |
| 57 |
7.011 |
6.443 |
5.395 |
3.904 |
60 |
| 58 |
5.853 |
4.846 |
3.548 |
2.210 |
61 |
Diketahui juga \({e_{60}} = 1\) dan kematian berdistribusi seragam pada setiap usia
Tentukan \(e_{\left[ {58} \right] + 2}^0\)
- 2,1
- 1,6
- 1,1
- 0,6
- 0,1
| Diketahui |
Berikut adalah select and ultimate life table dengan periode seleksi 3 tahun:
| \(\left[ x \right]\) |
\({l_{\left[ x \right]}}\) |
\({l_{\left[ x \right] + 1}}\) |
\({l_{\left[ x \right] + 2}}\) |
\({l_{\left[ x \right] + 3}}\) |
\(x + 3\) |
| 55 |
10.000 |
9.493 |
8.533 |
7.664 |
58 |
| 56 |
8.547 |
8.028 |
6.889 |
5.630 |
59 |
| 57 |
7.011 |
6.443 |
5.395 |
3.904 |
60 |
| 58 |
5.853 |
4.846 |
3.548 |
2.210 |
61 |
Diketahui juga \({e_{60}} = 1\) dan kematian berdistribusi seragam pada setiap usia |
| Rumus yang digunakan |
\(e_x^0 = {e_x} + 0.5\);
\({e_x} = {p_x} + {p_x} \cdot {e_{x + 1}}\); atau
\({e_{x + 1}} = \frac{{{e_x}}}{{{p_x}}} – 1\) \({}_t{p_x} = \frac{{{l_{x + t}}}}{{{l_x}}}\) |
| Proses pengerjaan |
\(e_{\left[ {58} \right] + 2}^0 = {e_{\left[ {58} \right] + 2}} + 0.5\)
\(e_{\left[ {58} \right] + 2}^0 = {p_{\left[ {58} \right] + 2}}\left( {1 + {e_{61}}} \right) + 0.5\)
\(e_{\left[ {58} \right] + 2}^0 = {p_{\left[ {58} \right] + 2}}\left( {1 + \frac{{{e_{60}}}}{{{p_{60}}}} – 1} \right) + 0.5\)
\(e_{\left[ {58} \right] + 2}^0 = \frac{{{l_{61}}}}{{{l_{\left[ {58} \right] + 2}}}}\left( {\frac{{{e_{60}}}}{{\frac{{{l_{61}}}}{{{l_{60}}}}}}} \right) + 0.5\)
\(e_{\left[ {58} \right] + 2}^0 = \frac{{2210}}{{3548}}\left( {1 \cdot \frac{{3904}}{{2210}}} \right) + 0.5\)
\(e_{\left[ {58} \right] + 2}^0 = 1.600338\) |
| Jawaban |
b. 1,6 |
