Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan sebagai berikut :
- \({q_x} = 0,1\)
- “force of mortality” adalah konstan antara “integral ages”
Hitunglah \({}_{0,5}{q_{x + 0,25}}\) (pembulatan terdekat)
- 0,051
- 0,043
- 0,032
- 0,026
- 0,012
| Rumus | \({l_{x + t}} = ({l_x}){({p_x})^t}\), untuk force of mortality |
| Pembahasan | \({}_{0,5}{q_{x + 0,25}} = 1 – {}_{0,5}{p_{x + 0,25}}\) \({}_{0,5}{q_{x + 0,25}} = 1 – \left( {\frac{{{l_{x + 0,75}}}}{{{l_{x + 0,25}}}}} \right)\) \({}_{0,5}{q_{x + 0,25}} = 1 – \left( {\frac{{{l_x}{{\left( {{p_x}} \right)}^{0,75}}}}{{{l_x}{{\left( {{p_x}} \right)}^{0,25}}}}} \right)\) \({}_{0,5}{q_{x + 0,25}} = 1 – \frac{{{{\left( {{p_x}} \right)}^{0,75}}}}{{{{\left( {{p_x}} \right)}^{0,25}}}}\) \({}_{0,5}{q_{x + 0,25}} = 1 – {({p_x})^{0,5}}\) \({}_{0,5}{q_{x + 0,25}} = 1 – {(1 – {q_x})^{0,5}}\) \({}_{0,5}{q_{x + 0,25}} = 1 – {(1 – 0,1)^{0,5}}\) \({}_{0,5}{q_{x + 0,25}} = 1 – {(0,9)^{0,5}}\) \({}_{0,5}{q_{x + 0,25}} = 0,05131670195\) \({}_{0,5}{q_{x + 0,25}} \cong 0,051\) |
| Jawaban | a. 0,051 |