Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Keuangan |
| Periode Ujian |
: |
Maret 2015 |
| Nomor Soal |
: |
25 |
SOAL
Nyatakan \({d^{\left( 4 \right)}}\) sebagai fungsi \({i^{\left( 3 \right)}}\)
- \(4\left[ {1 – {{\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)}^{ – \frac{3}{4}}}} \right]\)
- \(3\left[ {1 – {{\left( {1 + \frac{{{i^{(4)}}}}{4}} \right)}^{ – \frac{3}{4}}}} \right]\)
- \(4\left[ {1 + {{\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)}^{\frac{3}{4}}}} \right]\)
- \(3\left[ {1 + {{\left( {1 + \frac{{{i^{(4)}}}}{4}} \right)}^{ – \frac{3}{4}}}} \right]\)
- \(3\left[ {1 – {{\left( {1 + \frac{{{i^{(3)}}}}{4}} \right)}^{ – \frac{3}{4}}}} \right]\)
| Diketahui |
\({d^{\left( 4 \right)}}\) |
| Rumus yang digunakan |
\({\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)^3} = {\left( {1 – \frac{{{d^{(4)}}}}{4}} \right)^{ – 4}}\) |
| Proses pengerjaan |
\({\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)^3} = {\left( {1 – \frac{{{d^{(4)}}}}{4}} \right)^{ – 4}}\)
\({\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)^{ – \frac{3}{4}}} = 1 – \frac{{{d^{(4)}}}}{4}\)
\({d^{(4)}} = 4\left[ {1 – {{\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)}^{ – \frac{3}{4}}}} \right]\) |
| Jawaban |
a. \(4\left[ {1 – {{\left( {1 + \frac{{{i^{(3)}}}}{3}} \right)}^{ – \frac{3}{4}}}} \right]\) |
