Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Matematika Aktuaria |
Periode Ujian |
: |
Mei 2017 |
Nomor Soal |
: |
27 |
SOAL
Untuk suatu model “2-year selection and ultimate mortality”, diberikan:
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 96.815\)
- \({l_{77}} = 96.124\)
Hitunglah \({l_{\left[ {75} \right] + 1}}\)
- 96.150
- 96.780
- 97.420
- 98.050
- 98.690
Diketahui |
Untuk suatu model “2-year selection and ultimate mortality”, diberikan:
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 96.815\)
- \({l_{77}} = 96.124\)
|
Rumus yang digunakan |
\({}_t{p_x} = \frac{{{l_{x + t}}}}{{{l_x}}}\)
\({}_t{q_x} = \frac{{{l_x} – {l_{x + t}}}}{{{l_x}}}\) |
Proses pengerjaan |
\({p_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\)
\(1 – {q_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\)
\(1 – 0.95{q_{76}} = \frac{{{l_{77}}}}{{{l_{\left[ {75} \right] + 1}}}}\)
\({l_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{1 – 0.95\left( {\frac{{{l_{76}} – {l_{77}}}}{{{l_{76}}}}} \right)}}\)
\({l_{\left[ {75} \right] + 1}} = \frac{{96,124}}{{1 – 0.95\left( {\frac{{96,815 – 96,124}}{{96,815}}} \right)}} = 96,780.21414\) |
Jawaban |
B. 96.780 |