Pembahasan Soal Ujian Profesi Aktuaris
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 |