Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2014 |
| Nomor Soal |
: |
20 |
SOAL
Hitunglah \({p_{38}}\), bila diketahui sebagai berikut:
\({}_{23}^{20}{V_{15}} = 0,585\)
\({}_{24}^{20}{V_{15}} = 0,600\)
\(i = 0,08\)
- 0,8482
- 0,979
- 0,9205
- 0,9470
- 0,9709
| Diketahui |
\({}_{23}^{20}{V_{15}} = 0,585\)
\({}_{24}^{20}{V_{15}} = 0,600\)
\(i = 0,08\) |
| Rumus yang digunakan |
\(\left( {{}_k^h{V_x} + {b_{k + 1}} \cdot {P_k}} \right){\left( {1 + i} \right)^s} = {b_{k + 1}} \cdot {}_s{q_{x + k}} + {}_s{p_{x + k}} \cdot {}_{k + s}^h{V_x}\) |
| Proses pengerjaan |
\({}_{23}^{20}{V_{15}}\left( {1 + i} \right) = {q_{38}} + {p_{38}} \cdot {}_{24}^{20}{V_{15}}\)
\(0.585\left( {1.08} \right) = 1 – {p_{38}} + 0.6{p_{38}}\)
\({p_{38}} = \frac{{1 – 0.585\left( {1.08} \right)}}{{0.4}}\)
\({p_{38}} = 0.9205\) |
| Jawaban |
c. 0,9205 |
