Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
A60 – Matematika Aktuaria |
| Periode Ujian |
: |
Mei 2017 |
| Nomor Soal |
: |
1 |
SOAL
Dengan menggunakan “annual interest rate” \(i = 0,05\) dan \({l_{95}} = 100,{l_{96}} = 70,{l_{97}} = 40,{l_{98}} = 20,{l_{99}} = 4,{l_{100}} = 0\)
Hitunglah nilai dari:
- 0,932
- 1,123
- 1,235
- 1,455
- 2,012
| Rumus |
\({a_x} = \sum\limits_{t = 1}^\infty {{v^t}\,{}_t{p_x}} \)
\({}_t{P_x} = \frac{{{l_{95 + t}}}}{{{l_{95}}}}\) |
| Kalkulasi |
\({a_{95}} = \sum\limits_{t = 1}^\infty {{v^t}\,{}_t{p_{95}}} \)
\({a_{95}} = \sum\limits_{t = 1}^\infty {{v^t}\,\frac{{{l_{95 + t}}}}{{{l_{95}}}}} \)
\({a_{95}} = \frac{1}{{{l_{95}}}}\sum\limits_{t = 1}^\infty {{v^t}\,} {l_{95 + t}}\)
\({a_{95}} = \frac{1}{{100}}\left( {\frac{{{l_{96}}}}{{1,05}} + \frac{{{l_{97}}}}{{1,{{05}^2}}} + \frac{{{l_{98}}}}{{1,{{05}^3}}} + \frac{{{l_{99}}}}{{1,{{05}^4}}} + \frac{{{l_{100}}}}{{1,{{05}^5}}}} \right)\)
\({a_{95}} = \frac{1}{{100}}\left( {\frac{{70}}{{1,05}} + \frac{{40}}{{1,{{05}^2}}} + \frac{{20}}{{1,{{05}^3}}} + \frac{4}{{1,{{05}^4}}} + \frac{0}{{1,{{05}^5}}}} \right)\)
\({a_{95}} = \frac{1}{{100}}\left( {123,51541} \right)\)
\({a_{95}} = 1,2351541\)
\({a_{95}} \cong 1,235\) |
| Jawaban |
c. 1,235 |
