Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
April 2019 |
| Nomor Soal |
: |
8 |
SOAL
Diberikan informasi sebagai berikut:
- \({\delta _t} = \left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {0,04}\\ {0,03} \end{array}} {\begin{array}{*{20}{c}} {0 \le t \le 5}\\ {t > 5} \end{array}} \end{array}} \right.\)
- \(\mu = 0,01\)
Hitunglah \({\bar a_{x:\overline {\left. {10} \right|} }}\) (gunakan pembulatan terdekat)
- 7,95
- 8,95
- 9,95
- 10,45
- 11,45
| Diketahui |
Diberikan informasi sebagai berikut:
- \({\delta _t} = \left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {0,04}\\ {0,03} \end{array}} {\begin{array}{*{20}{c}} {0 \le t \le 5}\\ {t > 5} \end{array}} \end{array}} \right.\)
- \(\mu = 0,01\)
|
| Rumus yang digunakan |
\({\bar a_{x:\overline {\left. {n + m} \right|} }} = {\bar a_{x:\overline {\left. n \right|} }} + {}_n{E_x} \cdot {\bar a_{x + n:\overline {\left. m \right|} }}\)
Untuk \({\mu _{x + t}}\) dan \({\delta _t}\) konstan
\({\bar a_{x:\overline {\left. n \right|} }} = {\bar a_x}\left( {1 – {}_n{E_x}} \right) = \frac{{\left( {1 – \exp \left[ { – n\left( {\mu + \delta } \right)} \right]} \right)}}{{\mu + \delta }}\) |
| Proses pengerjaan |
\({{\bar a}_{x:\overline {\left. {10} \right|} }} = {{\bar a}_{x:\overline {\left. 5 \right|} }} + {}_5{E_x} \cdot {{\bar a}_{x + 5:\overline {\left. 5 \right|} }}\)
\({{\bar a}_{x:\overline {\left. {10} \right|} }} = \frac{{1 – \exp \left[ { – 5\left( {0.01 + 0.04} \right)} \right]}}{{0.01 + 0.04}} + \exp \left[ { – 5\left( {0.01 + 0.04} \right)} \right] \cdot \frac{{1 – \exp \left[ { – 5\left( {0.01 + 0.03} \right)} \right]}}{{0.01 + 0.03}}\)
\(= 7.9533\) |
| Jawaban |
a. 7,95 |
