Pembahasan Soal Ujian Profesi Aktuaris
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 |