Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
A60 – Matematika Aktuaria |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
4 |
SOAL
Diberikan sebagai berikut:
- \({q_x} = 0,5\)
- “Force of Mortality” adalah konstan antara “integral ages”
Hitunglah
- 0,2525
- 0,2626
- 0,2727
- 0,2828
- 0,2929
PEMBAHASAN
| Diketahui |
\(Force\,of\,Mortality\,:\) \({l_{x + t}} = {l_x}\,{({p_x})^t}\) |
| Kalkulasi |
\(\frac{1}{2}{q_x} + \frac{1}{4} = 1 – \frac{1}{2}{p_x} + \frac{1}{4}\)
\(\frac{1}{2}{q_x} + \frac{1}{4} = 1 – \frac{{{l_x} + \frac{3}{4}}}{{{l_x} + \frac{1}{4}}}\)
\(\frac{1}{2}{q_x} + \frac{1}{4} = 1 – \frac{{{l_x}{{({p_x})}^{{\textstyle{3 \over 4}}}}}}{{{l_x}({p_x}){\textstyle{1 \over 4}}}}\)
\(\frac{1}{2}{q_x} + \frac{1}{4} = 1 – ({p_x}){\textstyle{1 \over 2}}\)
\(\frac{1}{2}{q_x} + \frac{1}{2} = 1 – {(1 – {q_x})^{\frac{1}{2}}}\)
\(\frac{1}{2}{q_x} + \frac{1}{4} = 1 – (1 – 0,5){\textstyle{1 \over 2}}\)
\(\frac{1}{2}{q_x} + \frac{1}{4} = 0,2928932\)
\(\frac{1}{2}{q_x} + \frac{1}{4} \cong 0,2929\) |
| Jawaban |
e. 0,2929 |
