Pembahasan Soal Ujian Profesi Aktuaris
Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian | : | Matematika Aktuaria |
Periode Ujian | : | Mei 2018 |
Nomor Soal | : | 6 |
SOAL
Diketahui,
\({P_{x:\left. {\overline {\, 3 \,}}\! \right| }} = 0,35\) \(i = 0,06\) \({l_x} = 100\) \({l_{x + 1}} = 95\)
Hitunglah nilai \(10.000\left( {_2{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}{ – _1}{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}} \right)\)!
- 2.565
- 2.555
- 2.575
- 2.585
- 2.595
Diketahui | - \({P_{x:\left. {\overline {\, 3 \,}}\! \right| }} = 0,35\)
- \(i = 0,06\)
- \({l_x} = 100\)
- \({l_{x + 1}} = 95\)
|
Rumus | \(\left( {_{t – 1}V + P} \right)\left( {1 + i} \right) = {q_{x + t – 1}} + {p_{x + t – 1}}\left( {_tV} \right)\) |
Step 1 | \({q_x} = \frac{{{l_x} – {l_{x + 1}}}}{{{l_x}}} = \frac{{100 – 95}}{{100}} = 0,05\)
Mencari \(_1{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}\)
\(\left( {_0V + 0,35} \right)\left( {1,06} \right) = 0,05 + 0,95\left( {_1V} \right)\)
\(0,321 = 0,95\left( {_1V} \right)\)
\(_1V = 0,337894736\)
Mencari \(_2{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}\)
\(\left( {_2V + P} \right)\left( {1 + i} \right) = 1\)
\(\left( {_2V + 0,35} \right)\left( {1,06} \right) = 1\)
\(_2V + 0,35 = 0,943396226\)
\(_2V = 0,593396226\)
|
Step 2 | \(10.000\left( {_2{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}{ – _1}{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}} \right)\) …?
\(= 10.000\left( {0,593396226 – 0,337894736} \right)\)
\(= 2.555\) |
Jawaban | b. 2.555 |