25 April, 2024

Pembahasan Ujian PAI: A60 – No. 19 – Juni 2015

31 October 2019

by Fery Widhiatmoko

with no comment

A60 - Matematika Aktuaria Aktuaria Edukasi Pembahasan Ujian Profesi Aktuaris (Persatuan Aktuaris Indonesia / PAI)

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Matematika Aktuaria
Periode Ujian	:	Juni 2015
Nomor Soal	:	19

SOAL

Untuk suatu tabel double decrement, diberikan:

Hitunglah

\(\frac{1}{4}\)
\(\frac{1}{5}\)
\(\frac{1}{6}\)
\(\frac{1}{7}\)
\(\frac{1}{8}\)

Diketahui	\({}_{\left. 1 \right\|}q_x^{\left( 1 \right)} = \frac{1}{4}\) \(q_{x + 1}^{\left( 1 \right)} = \frac{1}{3}\)
Rumus yang digunakan	\({}_{\left. t \right\|u}q_x^{\left( j \right)} = {}_tp_x^{\left( \tau \right)} \cdot {}_uq_{x + t}^{\left( j \right)}\) \({}_tp_x^{\left( \tau \right)} = \prod\limits_{j = 1}^n {{}_tp_x^{‘\left( j \right)}} = \prod\limits_{j = 1}^n {\left( {1 – {}_tq_x^{‘\left( j \right)}} \right)} \)
Proses pengerjaan	\({}_{\left. 1 \right\|}q_x^{\left( 1 \right)} = p_x^{\left( \tau \right)} \cdot q_{x + 1}^{\left( 1 \right)}\) \(\frac{1}{4} = \frac{1}{3}p_x^{\left( \tau \right)}\) \(p_x^{\left( \tau \right)} = \frac{3}{4}\)
Jawaban	d. \(\frac{1}{7}\)