Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | November 2015 |
| Nomor Soal | : | 16 |
SOAL
Jika \({l_x} = 14.040\) dan \({q_x} = \frac{1}{3}\), hitunglah \({l_{x + \frac{1}{4}}}\) berdasarkan asumsi hiperbolis
- 12.480
- 13.440
- 14.238
- 11.220
- 12.230
| Diketahui | \({l_x} = 14.040\) dan \({q_x} = \frac{1}{3}\) |
| Rumus yang digunakan | \({l_{x + s}} = {\left( {\frac{s}{{{l_{x + 1}}}} + \frac{{1 – s}}{{{l_x}}}} \right)^{ – 1}}\)
\({q_x} = \frac{{{l_x} – {l_{x + 1}}}}{{{l_x}}}\) |
| Proses pengerjaan | \({q_x} = \frac{{{l_x} – {l_{x + 1}}}}{{{l_x}}}\)
\(\frac{1}{3} = \frac{{14.040 – {l_{x + 1}}}}{{14.040}}\)
\(14.040 = 42.120 – 3{l_{x + 1}}\)
\({l_{x + 1}} = \frac{{28.080}}{3}\)
\(= 9.360\) |
| \({l_{x + \frac{1}{4}}} = {\left( {\frac{{0,25}}{{9.360}} + \frac{{1 – 0,25}}{{14.040}}} \right)^{ – 1}}\)
\(= {\left( {\frac{1}{{12.480}}} \right)^{ – 1}}\)
\(= 12.480\) |
| Jawaban | a. 12.480 |
