Fin_9.tex

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\begin{document}
    \begin{center}
        \LARGE\textbf{MTH6121 Introduction to Mathematical Finance}\\
        Coursework 7
    \end{center}
    Please hand in your solution of the \textbf{starred} exercises by \textbf{17.00 on Wednesday 23 November 2016} using the green Introduction to Mathematical Finance Collection Box on the second floor of the Mathematics Building. Don’t forget to put your \textbf{name} (with your \underline{surname} underlined), \textbf{student number} and your \textbf{tutorial group} on your solutions, and to \textbf{staple} them.\par
    %
    \textbf{Exercise 1.} After graduation, you have two job offers. Both jobs are in the UK and for a fixed term of $3$ years. Company A offers you $32000$ pounds at the end of the first year, $33000$ pounds at the end of the second year, and $36000$ pounds at the end of your final year. Company B offers you a ‘golden hello’ of $6000$ pounds when you start the job, and then a constant salary of $31000$ pounds at the end of each year. The current interest rate in the UK is $5.5\%$ and the current inflation rate $4.0\%$. You should assume that these rates remain unchanged during the $3$ years. Which offer is the better deal? Give reasons.\par
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    \textbf{Exercise* 2.} Consider a four-year investment that, for an initial payment of $1000$ pounds, produces the following returns: $500$ pounds at the end of the second year, $750$ pounds at the end of the fourth year, and nothing at the end of the first and third years.
    \begin{enumerate}[(a)]
        \item  What is the internal rate of return of this investment?
        \item What is the internal rate of return of this investment if it is subject to $18\%$ capital gains tax payable at the end of the fourth year?
    \end{enumerate}
    %
    \textbf{Exercise 3.} Suppose that interest is compounded continuously at rate
    $$
    r(t)
    =
    \begin{cases}
        at & \text{if}\ 0 \leq t \leq 1,\\
        a& \text{IF}\  > 1,
    \end{cases}
    $$
    where a is constant with $0 < a < 1$.
    \begin{enumerate}
        \item Draw a sketch of $r(t)$.
        \item Determine the present value of \pounds$2, 000$ to be received in $3$ years time.
    \end{enumerate}
\end{document}