Hogwarts Life offers a pension plan that pays a lump sum benefit of 750,000 at the end of the
year of death while employed or 450,000 at the end of the year of retirement.
Given that:
\begin{itemize}
\item Multiple decrement table, where decrement 1 is retirement and decrement 2 is death:
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & $l_x^{\tau}$ & $d_x^{(1)}$ & $d_x^{(2)}$ \\ \hline
60 & 100,000 & 9,800 & 950 \\ \hline
61 & 89,250 & 21,000 & 1,250 \\ \hline
62 & 67,000 & 65,770 & 1,230 \\ \hline
\end{tabular}
\item Interest rate: 6\% per annum.
\item Salary Scale (as attached)
\end{itemize}
(b) Harry, a senior manager in Hogwarts Life currently aged 60, plan to retire before age 63.
Calculate the expected present value of the retirement benefit.
(6 marks)
(c) Calculate the expected present value of the death in service benefit.
(6 marks)
Hogwarts Life decide to change their death in service benefit to its employee. The death
benefits would be triple the annual salary rate at death. At age 60, Harry's salary rate is
\$250,000 per year. If deaths occur evenly throughout the year,
(d) Estimate the expected present value of the death in service benefits.
