28 April, 2024

Pembahasan Ujian PAI: A60 – No. 9 – November 2015

23 September 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	:	November 2015
Nomor Soal	:	9

SOAL

Diberikan suatu rate kematian sebagai berikut

\({q_{75}} = 0,01\) \({q_{76}} = 0,02\) \({q_{77}} = 0,04\) \(i = 0,05\)

Hitunglah \({\ddot a_{75:\left. {\overline {\, 3 \,}}\! \right| }}\) (pembulatan terdekat)

by Auditya Brilliant Asuransi Umum

by Abinaila Taim A10 - Matematika Keuangan

by Abinaila Taim A10 - Matematika Keuangan

by Ir. Sudarno Hardjo Saparto AAIK, ICPU, ICBU, QIP, CIIB, AMRP, AK3 Asuransi Kebakaran

by Agus Sofian Eka Hidayat, S.Pd., M.Ed., M.Sc. Asuransi Umum

by Abinaila Taim Dana Pensiun

©

2024

Diketahui	\({q_{75}} = 0,01\) \({q_{76}} = 0,02\) \({q_{77}} = 0,04\) \(i = 0,05\)
Rumus yang digunakan	\({}_t{p_x} = \prod\limits_{k = 0}^{t – 1} {{p_{x + k}}} \) \({\ddot a_{x:\left. {\overline {\, n \,}}\! \right\| }} = \sum\limits_{k = 0}^{n – 1} {{v^k}{}_k{p_x}} \)
Proses pengerjaan	\({{\ddot a}_{75:\left. {\overline {\, 3 \,}}\! \right\| }} = \sum\limits_{k = 0}^2 {{v^k}{}_k{p_x}} = {v^0}{}_0{p_{75}} + {v^1}{}_1{p_{75}} + {v^2}{}_2{p_{75}}\) \({{\ddot a}_{75:\left. {\overline {\, 3 \,}}\! \right\| }} = {v^0}{}_0{p_{75}} + {v^1}{p_{75}} + {v^2}{p_{75}}{p_{76}}\) \({{\ddot a}_{75:\left. {\overline {\, 3 \,}}\! \right\| }} = 1 + \frac{{\left( {1 – 0.01} \right)}}{{1.05}} + \frac{{\left( {1 – 0.01} \right)\left( {1 – 0.02} \right)}}{{{{1.05}^2}}}\) \({{\ddot a}_{75:\left. {\overline {\, 3 \,}}\! \right\| }} = 2.822857\)
Jawaban	c. 2,82