Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
April 2019 |
| Nomor Soal |
: |
28 |
SOAL
Diberikan informasi sebagai berikut:
- \({q_{60}} = 0,01\)
- Dengan menggunakan \(i = 0,05\); \({A_{60:\overline {\left. 3 \right|} }} = 0,86545\)
Hitunglah \({A_{60:\overline {\left. 3 \right|} }}\) dengan menggunakan \(i = 0,045\) (gunakan pembulatan terdekat)
- 0,866
- 0,870
- 0,874
- 0,878
- 0,882
| Diketahui |
Diberikan informasi sebagai berikut:
- \({q_{60}} = 0,01\)
- Dengan menggunakan \(i = 0,05\); \({A_{60:\overline {\left. 3 \right|} }} = 0,86545\)
|
| Rumus yang digunakan |
\(A_{x:\overline {\left. n \right|} }^1 = b\sum\limits_{k = 0}^{n – 1} {{v^{k + 1}}{}_k{p_x}{q_{x + k}}} \) |
| Proses pengerjaan |
\({A_{60:\overline {\left. 3 \right|} }} = \sum\limits_{k = 0}^2 {{v^{k + 1}}{}_k{p_{60}}{q_{60 + k}}} \)
\({A_{60:\overline {\left. 3 \right|} }} = v{q_{60}} + {v^2}{p_{60}}{q_{61}} + {v^3}{}_2{p_{60}}{q_{62}}\)
\({A_{60:\overline {\left. 3 \right|} }} = v{q_{60}} + {v^2}\left( {1 – {q_{60}}} \right){q_{61}} + {v^3}\left( {1 – {q_{60}}} \right)\left( {1 – {q_{61}}} \right){q_{62}}\)
\({A_{60:\overline {\left. 3 \right|} }} = {q_{60}}v + \left( {1 – {q_{60}}} \right){q_{61}}{v^2} + \left( {1 – {q_{60}}} \right){q_{62}}{v^3} – \left( {1 – {q_{60}}} \right){q_{61}}{q_{62}}{v^3}\)
\({q_{61}} = \frac{{{A_{60:\overline {\left. 3 \right|} }} – {q_{60}}v – \left( {1 – {q_{60}}} \right){q_{62}}{v^3}}}{{\left( {1 – {q_{60}}} \right){v^2} – \left( {1 – {q_{60}}} \right){q_{62}}{v^3}}}\)
\({q_{61}} = \frac{{0.086545 – \frac{{0.01}}{{1.05}} – \frac{{0.99\left( 1 \right)}}{{{{1.05}^3}}}}}{{\frac{{0.99}}{{{{1.05}^2}}} – \frac{{0.99\left( 1 \right)}}{{{{1.05}^3}}}}} = 0.017\) |
| \(A_{60:\overline {\left. 3 \right|} }^{revised} = {q_{60}}{v^{revised}} + \left( {1 – {q_{60}}} \right){q_{61}}{v^{revise{d^2}}} + \left( {1 – {q_{60}}} \right)\left( {1 – {q_{61}}} \right){q_{62}}{v^{revise{d^3}}}\)
\(A_{60:\overline {\left. 3 \right|} }^{revised} = \frac{{0.01}}{{1.045}} + \frac{{0.99\left( {0.017} \right)}}{{{{1.045}^2}}} + \frac{{0.99\left( {0.983} \right)\left( 1 \right)}}{{{{1.045}^3}}}\)
\(A_{60:\overline {\left. 3 \right|} }^{revised} = 0.8777\) |
| Jawaban |
d. 0,878 |
q62 nya dpt dr mana yah knpa bisa segitu? terimakasih