Pembahasan Ujian PAI: A60 - No. 26 - November 2016

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Matematika Aktuaria
Periode Ujian	:	November 2016
Nomor Soal	:	26

SOAL

Diberikan suatu “survival function”

\({S_0}\left( x \right) = \frac{1}{{1 + \sqrt x }}\)

Hitunglah \({}_{\left. 5 \right|10}{q_{15}}\)

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Diketahui	\({S_0}\left( x \right) = \frac{1}{{1 + \sqrt x }}\)
Rumus yang digunakan	\({}_{\left. t \right\|u}{q_x} = {}_t{p_x} – {}_{t + u}{p_x}\) \({}_t{p_x} = {S_x}\left( t \right) = \frac{{{S_0}\left( {x + t} \right)}}{{{S_0}\left( x \right)}}\)
Proses pengerjaan	\({}_t{p_x} = \frac{{{S_0}\left( {x + t} \right)}}{{{S_0}\left( x \right)}}\) \({}_t{p_x} = \frac{{\frac{1}{{1 + \sqrt {x + t} }}}}{{\frac{1}{{1 + \sqrt x }}}}\) \({}_t{p_x} = \frac{{1 + \sqrt x }}{{1 + \sqrt {x + t} }}\) \({}_5{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }}\) \({}_{15}{p_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {30} }}\) \({}_{\left. 5 \right\|10}{q_{15}} = {}_5{p_{15}} – {}_{15}{p_{15}}\) \({}_{\left. 5 \right\|10}{q_{15}} = \frac{{1 + \sqrt {15} }}{{1 + \sqrt {20} }} – \frac{{1 + \sqrt {15} }}{{1 + \sqrt {30} }}\) \({}_{\left. 5 \right\|10}{q_{15}} = 0.1381827\)
Jawaban	E. 0,14

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Pembahasan Ujian PAI: A60 – No. 26 – November 2016