Pembahasan Soal Ujian Profesi Aktuaris
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 |