Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan:
- Kematian berdistribusi seragam untuk setiap tahun usia
- \(i = 0,10\)
- \({q_x} = 0,05\)
- \({q_{x + 1}} = 0,06\)
Hitunglah
- 0,097
- 0,108
- 0,111
- 0,114
- 0,119
PEMBAHASAN
| Rumus | \({A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} = \sum\limits_{k = 1}^2 {{v^k}\,{}_{k – 1|}{q_x}} \) \({\bar A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} = \frac{i}{\delta }{A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }}\) |
| Step 1 | \({A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} = v\,{q_x} + {v^2}{p_x}\,{q_{x + 1}}\) \({A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} = \frac{{0,05}}{{1,1}} + \frac{{(1 – 0,05)(0,06)}}{{1,{1^2}}}\) \({A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} ={\rm{0,09256}}\) |
| Step 2 | \({\bar A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} = \frac{{0,1}}{{\ln (1 + 0,1)}}({\rm{0,09256}})\) \({\bar A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} ={\rm{0,09711}}\) \({\bar A_{\mathop x\limits^| :\left. {\overline {\, 2 \,}}\! \right| }} \cong {\rm{0,097}}\) |
| Jawaban | a. 0,097 |