Pembahasan Ujian PAI: A60 – No. 10 – Juni 2016

1. \(Z\left( n \right)\) adalah “present value random variabel for n-year term insurance on a life age \(x\)” berdasarkan yield curve sekarang
2. \(E\left[ {Z\left( 1 \right)} \right] = 0,014354\) dan \(E\left[ {Z\left( 2 \right)} \right] = 0,032308\)
3. “current one-year spot rate” adalah 4,50%
4. \({q_{x + 1}} = 0,02\)

\(E\left[ {Z\left( 2 \right)} \right] = \sum\limits_{k = 0}^1 {{v^{k + 1}} \cdot {}_k{p_x} \cdot {q_{x + k}}} = {v_{4.5\% }} \cdot {q_x} + {v^2} \cdot {p_x} \cdot {q_{x + 1}}\)
\(0.032308 = 0.014354 + \frac{{\left( {0.985} \right)\left( {0.02} \right)}}{{{{\left( {1 + i} \right)}^2}}}\)
\(i = \sqrt {\frac{{\left( {0.985} \right)\left( {0.02} \right)}}{{0.032308 – 0.014354}}} – 1\)
\(i = 0.0475 = 4.75\% \)