Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | Juni 2016 |
| Nomor Soal | : | 16 |
SOAL
Diberikan :
- Kematian berdistribusi seragam untuk setiap tahun usia
- \(i = 0,10\)
- \({q_x} = 0,05\)
- \({q_{x + 1}} = 0,08\)
Hitunglah \({\bar A_{x:\left. {\overline {\, 2 \,}}\! \right| }}\) (pembulatan terdekat)
- 0,103
- 0,108
- 0,111
- 0,114
- 0,119
| Step 1 | \({A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = \sum\limits_{k = 0}^1 {{v^{k(x) + 1}}\Pr (} K(x) = k)\)
\({A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = v({q_x}) + {v^2}{p_x}{q_{x + 1}}\)
\({A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = {(1,1)^{ – 1}}(0,05) + {(1,1)^{ – 2}}(0,95)(0.08)\)
\({A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = 0,108264462\) |
| Step 2 | \({\bar A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = \frac{i}{\delta }{A_{x:\left. {\overline {\, 2 \,}}\! \right| }}\)
\({\bar A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = \frac{{0,1}}{{\ln (1,1)}}0,1082644628\)
\({\bar A_{x:\left. {\overline {\, 2 \,}}\! \right| }} = 0,1135917098\)
\({\bar A_{x:\left. {\overline {\, 2 \,}}\! \right| }} \cong 0,114\) |
| Jawaban | d. 0,114 |
