Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2015 |
| Nomor Soal | : | 13 |
SOAL
Manakah diantara pernyataan berikut yang benar?
- \(\frac{{{P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = d\)
- \(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = i\)
- \(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = v\)
- 1
- 1, 2
- 1, 3
- 2, 3
- 1, 2, 3
| Diketahui | - \(\frac{{{P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = d\)
- \(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = i\)
- \(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = v\)
|
| Rumus yang digunakan | \({P_x} = \frac{{d{A_x}}}{{1 – {A_x}}}\); \(1 – d = v\); \(v = \frac{1}{{1 + i}}\); \(d = \frac{i}{{1 + i}}\) |
| Proses pengerjaan | Untuk (1)
\({P_x} = \frac{{d{A_x}}}{{1 – {A_x}}}\)
\(\frac{{{P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = d\) (Benar) |
| Untuk (2)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{{\frac{{d{A_x}}}{{1 – {A_x}}}}}{{{A_x} – \frac{{d{A_x}}}{{1 – {A_x}}}\left( {1 – {A_x}} \right)}}\)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{{d{A_x}}}{{\left( {1 – {A_x}} \right)\left( {{A_x} – d{A_x}} \right)}}\)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{{d{A_x}}}{{\left( {1 – {A_x}} \right)\left( {1 – d} \right){A_x}}}\)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{d}{{\left( {1 – {A_x}} \right)v}}\)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{{\frac{i}{{1 + i}}}}{{\left( {1 – {A_x}} \right)\left( {\frac{1}{{1 + i}}} \right)}}\)
\(\frac{{{P_x}}}{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}} = \frac{i}{{1 – {A_x}}}\) (Salah) |
| Untuk (3)
\(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = \frac{{{A_x} – \frac{{d{A_x}}}{{1 – {A_x}}}\left( {1 – {A_x}} \right)}}{{{A_x}}}\)
\(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = \frac{{{A_x} – d{A_x}}}{{{A_x}}}\)
\(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = \frac{{\left( {1 – d} \right){A_x}}}{{{A_x}}}\)
\(\frac{{{A_x} – {P_x}\left( {1 – {A_x}} \right)}}{{{A_x}}} = v\) (Benar) |
| Jawaban | c. 1, 3 |
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