Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Sebuah produk anuitas whole life ditunda 30 tahun (30 years deferred whole life annuity) di jual kepada seorang berusia 35 tahun. Bila meninggal selama masa penundaan, maka premi tunggal neto dikembalikan tanpa bunga. Berapakah premi tunggal neto dari produk ini? Diketahui:
\[\begin{array}{l}
{{\ddot a}_{65}} = 9,90\\
{A_{35:\left. {\overline {\,
{30} \,}}\! \right| }} = 0,21\\
A_{35:\left. {\overline {\,
{30} \,}}\! \right| }^1 = 0,07
\end{array}\]
- 0,87722
- 1,49032
- 2,23548
- 1,75443
- 2,87722
PEMBAHASAN
Asumsi P adalah premi tunggal neto
Diketahui:
\({{\ddot a}_{65}} = 9,90\)
\({A_{35:\left. {\overline {\, {30} \,}}\! \right| }} = 0,21\)
\(A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1 = 0,07\)
Sehingga didapatkan:
\(_{30}{E_{35}} = {A_{35:\left. {\overline {\, {30} \,}}\! \right| }} – A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1\)
\(_{30}{E_{35}} = 0,21 – 0,07 = 0,14\)
Maka:
\(P = \left. {_{30}} \right|{{\ddot a}_{35}} + P \cdot A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1\)
\(P{ = _{30}}{E_{35}} \cdot {{\ddot a}_{65}} + P \cdot A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1\)
\(P – P \cdot A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1{ = _{30}}{E_{35}} \cdot {{\ddot a}_{65}}\)
\(P(1 – A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1){ = _{30}}{E_{35}} \cdot {{\ddot a}_{65}}\)
\(P = \frac{{_{30}{E_{35}} \cdot {{\ddot a}_{65}}}}{{(1 – A_{35:\left. {\overline {\, {30} \,}}\! \right| }^1)}}\)
\(P = \frac{{(0,14) \cdot (9,90)}}{{(1 – 0,07)}}\)
\(P = \frac{{1,386}}{{0,93}} = 1,49032\)
Jawaban: B. 1,49032