Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | November 2018 |
| Nomor Soal | : | 17 |
SOAL
Tentukan \({}_{20}{V_{45}}\) jika diketahui:
- 0,21
- 0,23
- 0,25
- 0,27
- 0,29
| Maka | \({}_{20}{V_{45}} = {P_{45}}\frac{{{{\ddot a}_{45:\left. {\overline {\, {20} \,}}\! \right| }}}}{{{}_{20}{E_{45}}}} – \frac{{{A_{\mathop {45}\limits^| :\left. {\overline {\, {20} \,}}\! \right| }}}}{{{}_{20}{E_{45}}}}\) \({}_{20}{V_{45}} = {P_{45}}\frac{1}{{{P_{45:\mathop {\left. {\overline {\, {20} \,}}\! \right| }\limits^| }}}} – \frac{{{A_{45:\left. {\overline {\, {20} \,}}\! \right| }} – {A_{45:\mathop {\left. {\overline {\, {20} \,}}\! \right| }\limits^| }}}}{{{}_{20}{E_{45}}}}\left( {\frac{{{{\ddot a}_{45:\left. {\overline {\, {20} \,}}\! \right| }}}}{{{{\ddot a}_{45:\left. {\overline {\, {20} \,}}\! \right| }}}}} \right)\) \({}_{20}{V_{45}} = {P_{45}}\frac{1}{{{P_{45:\mathop {\left. {\overline {\, {20} \,}}\! \right| }\limits^| }}}} – \frac{{{P_{45:\left. {\overline {\, {20} \,}}\! \right| }} – {P_{45:\mathop {\left. {\overline {\, {20} \,}}\! \right| }\limits^| }}}}{{{P_{45:\mathop {\left. {\overline {\, {20} \,}}\! \right| }\limits^| }}}}\) \({}_{20}{V_{45}} = (0,014)\frac{1}{{0,022}} – \frac{{0,03 – 0,022}}{{0,022}}\) \({}_{20}{V_{45}} = \frac{3}{{11}}\,\,\) \({}_{20}{V_{45}} = 0,27\) |
| Jawaban | d. 0,27 |