Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
19 |
SOAL
Diberikan suatu “survival function”
\({S_0}(x) = \frac{1}{{1 + \sqrt x }}\)
Hitunglah \({}_{5|15}{q_{15}}\)
- 0,176
- 0,186
- 0,196
- 0,206
- 0,216
| Rumus |
\({}_{5|15}{q_{15}} = {}_5{p_{15}}\,\,{}_{15}{q_{20}}\) |
| Step 1 |
\({}_{5|15}{q_{15}} = \frac{{{S_0}(20)}}{{{S_0}(15)}}\,\,\left( {1 – \frac{{{S_0}(35)}}{{{S_0}(20)}}\,} \right)\)
\({}_{5|15}{q_{15}} = \frac{{{S_0}(20)}}{{{S_0}(15)}}\,\,\left( {\frac{{{S_0}(20)}}{{{S_0}(20)}} – \frac{{{S_0}(35)}}{{{S_0}(20)}}\,} \right)\)
\({}_{5|15}{q_{15}} = \frac{{{S_0}(20) – {S_0}(35)}}{{{S_0}(15)}}\) |
| Step 2 |
\({S_0}(x) = \frac{1}{{1 + \sqrt x }}\)
\({}_{5|15}{q_{15}} = \frac{{\frac{1}{{1 + \sqrt {20} }} – \frac{1}{{1 + \sqrt {35} }}}}{{\frac{1}{{1 + \sqrt {15} }}}}\)
\({}_{5|15}{q_{15}} = {\rm{0}}{\rm{,18592}}\)
\({}_{5|15}{q_{15}} \cong {\rm{0}}{\rm{,186}}\) |
| Jawaban |
b. 0,186 |
