Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
A60 – Matematika Aktuaria |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
21 |
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 |
