Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan sebagai berikut:
- \({{\mu _{x + t}} = 0,01;}\) \({0 \le t < 5}\)
- \({{\mu _{x + t}} = 0,02;}\) \({5 \le t}\)
- \(\delta = 0,06\)
Hitunglah \({\bar a_x}\) (pembulatan terdekat)
- 12,5
- 13,0
- 13,4
- 13,9
- 14,3
| Diketahui |
|
| Rumus yang digunakan | Untuk \(\delta \) konstan \({{\bar a}_x} = {{\bar a}_{x:\left. {\overline {\, n \,}}\! \right| }} + {}_{\left. n \right|}{{\bar a}_x}\) \({{\bar a}_{x:\left. {\overline {\, n \,}}\! \right| }} = {{\bar a}_x}\left( {1 – {}_n{E_x}} \right) = \frac{{1 – \exp \left[ { – n\left( {\mu + \delta } \right)} \right]}}{{\mu + \delta }}\) \({}_{\left. n \right|}{{\bar a}_x} = {}_n{E_x} \cdot {{\bar a}_x} = \frac{{\exp \left[ { – n\left( {\mu + \delta } \right)} \right]}}{{\mu + \delta }}\) |
| Proses pengerjaan | Bagi annuitas \({\bar a_x}\) menjadi 2 bagian annuitas yaitu 5-years temporary life dan 5 years deffered life.
|
| \({\bar a_x} = {\bar a_{x:\left. {\overline {\, 5 \,}}\! \right| }} + {}_{\left. 5 \right|}{\bar a_x} = 4.21874 + 8.80860 = 13.0273\) | |
| Jawaban | b. 13,0 |