Pembahasan Ujian PAI: A60 - No. 6 - Mei 2018

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 \(10.000\left( {_2{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}{ – _1}{V_{x:\left. {\overline {\, 3 \,}}\! \right| }}} \right)\)!

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