Pembahasan Ujian PAI: A60 – No. 1 – Mei 2018

• \({q_x} = 0,01\)
• \({q_{x + 1}} = 0,02\)
• \(i = 0,05\)
• saat t=1 Benefitnya sebesar 500.000, Preminya sebesar P
• saat t=2 Benefitnya sebesar , Preminya sebesar 1,1P

Mencari APV Premi
APV Premi \(= P \cdot {\ddot a_{x:\left. {\overline {\,  2 \,}}\! \right| }}\)

\(= P \cdot \sum\limits_0^1 {{v^n} \cdot nPx} \)
\(= P \cdot \left[ {\left( {{{1,05}^0}{ \cdot _0}{P_x}} \right) + \left( {{{1,05}^{ – 1}}{ \cdot _1}{P_x} \cdot 1,1} \right)} \right]\)
\(= P \cdot \left[ {1 + \left( {{{1,05}^{ – 1}} \cdot 0,99 \cdot 1,1} \right)} \right]\)
\(= 2,037142857P\)

\(= 500.000 \cdot \sum\limits_0^1 {{v^{k + 1}} \cdot \Pr \left( {{k_{\left( x \right)}} = k} \right)} \)
\(= 500.000 \cdot \left( {v \cdot {q_x} + {v^2} \cdot {p_x} \cdot {q_{x + 1}} \cdot 1,1} \right)\)
\(= 500.000 \cdot \left( {\left( {{{1,05}^{( – 1)}} \cdot 0,01} \right) + \left( {{{1,05}^{( – 2)}} \cdot 0,99 \cdot 0,02 \cdot 1,1} \right)} \right)\)
\(= 500.000 \cdot \left( {0,00952381 + 0,019755102} \right)\)
\(= 14.639,456\)

APV PREMI = APV BENEFIT

\(2,037142857P = 14.639,456\)
\(P = 7.186,2687 \simeq 7.186\)