Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Matematika Aktuaria |
Periode Ujian |
: |
November 2015 |
Nomor Soal |
: |
2 |
SOAL
Untuk suatu model “2-year selection and ultimate mortality”, diberikan:
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 98.153\)
- \({l_{77}} = 96.124\)
Hitunglah \({l_{\left[ {75} \right] + 1}}\) (pembulatan terdekat)
- 96.150
- 96.780
- 97.420
- 98.050
- 98.690
Diketahui |
- \({q_{\left[ x \right] + 1}} = 0,95{q_{x + 1}}\)
- \({l_{76}} = 98.153\)
- \({l_{77}} = 96.124\)
|
Rumus yang digunakan |
\({q_x} = 1 – {p_x} = 1 – \frac{{{l_{x + 1}}}}{{{l_x}}}\) dan \({p_{\left[ x \right] + 1}} = \frac{{{l_{x + 2}}}}{{{l_{\left[ x \right] + 1}}}}\) |
Proses pengerjaan |
\({q_{76}} = 1 – \frac{{{l_{77}}}}{{{l_{76}}}} = 1 – \frac{{96,124}}{{98,153}} = 0.020672\) |
\({q_{\left[ {75} \right] + 1}} = 0.95{q_{76}} = 0.95\left( {0.020672} \right) = 0.019638\) |
\({l_{\left[ {75} \right] + 1}} = \frac{{{l_{77}}}}{{{p_{\left[ {75} \right] + 1}}}} = \frac{{96,124}}{{1 – 0.019638}} = 98,050\) |
Jawaban |
d. 98.050 |