Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Agustus 2023 |
| Nomor Soal | : | 7 |
SOAL
Untuk sebuah tabel double decrement, diberikan:
| Usia \(x\) | \(l_x^{(T)}\) | \(d_x^{(1)}\) | \(d_x^{(2)}\) |
| 55 | 700 | 40 | 35 |
| 56 | – | – | 60 |
| 57 | 475 | – | – |
Setiap decrement menyebar secara uniform, hitunglah nilai
a. 0,848
b. 0,766
c. 0,600
d. 0,427
e. 0,152
| Diketahui | tabel double decrement :| Usia \(x\) | \(l_x^{(T)}\) | \(d_x^{(1)}\) | \(d_x^{(2)}\) | | 55 | 700 | 40 | 35 | | 56 | – | – | 60 | | 57 | 475 | – | – |
|
| Rumus yang digunakan | Formula,- \(P’^{(1)}_x = \left( P_x^{(T)} \right)^{d_x^{(1)} / d_x^{(T)}}\)
- \(d_x^{(T)} = d_x^{(1)} + d_x^{(2)}\)
- \(l_{x+1}^{(T)} = l_x^{(T)} – d_x^{(T)}\)
- \(P_x^{(T)} = \dfrac{l_{x+1}^{(T)}}{l_x^{(T)}}\)
|
| Proses pengerjaan | | Usia \(x\) | \(l_x^{(T)}\) | \(d_x^{(1)}\) | \(d_x^{(2)}\) | | 55 | 700 | 40 | 35 | | 56 | \(l_{56}^{(T)}\) | \(d_{56}^{(1)}\) | 60 | | 57 | 475 | – | – |
- \(l_{56}^{\left( T \right)} = 700 – 40 – 35\)
\(l_{56}^{\left( T \right)} = 625\)- \(d_{56}^{\left( 1 \right)} = 625 – 475 – 60\)
\(d_{56}^{\left( 1 \right)} = 90\)- \(p’^{(1)}_{56} = \left( p_{56}^{(T)} \right)^{d_{56}^{(1)} / d_{56}^{(T)}}\)
\(p’^{(1)}_{56} = \left( \dfrac{475}{625} \right)^{90 / (90+60)}\)jadi \(p’^{(1)}_{56} = 0{,}848180\) |
| Jawaban | a. 0,848 |
