\documentclass[12pt]{article}
\usepackage{fullpage,amsmath,amsfonts}

\begin{document}

\title{Derivatives Lab}
\author{Session 2}
\date{September 6, 2011}
\maketitle

\begin{enumerate}

\item (From Ross, p.\ 45.) An individual who plans to retire in 20
years has decided to put an amount $A$ in the bank at the beginning of
each of the next 240 months, after which she will withdraw EUR 1000
at the beginning of each of the following 360 months.  Assuming a
nominal yearly interest rate of 6\% compounded monthly, how large does
$A$ need to be?

\item Write a Python program which prints out an amortization schedule
for a mortgage. 

The program should take as input the nominal yearly interest
rate $r$, the amount of the loan $P$, the number of compounding
periods per annum $m$, and the term of the mortgage $n$ in years.
Assume that the mortgage is fully redeemed at the end of the term.

The program should compute the monthly payment, the effective annual
interest rate, and a detailed payment schedule listing, for each
month, the interest and principal parts of the payment and the
remaining principal.

\item Find a closed form formula for the remaining principal right
after the $k$th mortgage payment.

\item An investment sold at price $P$ is guaranteeing a cash flow
$C_1, \dots, C_N$ at the end of each year.  Write a program to compute
its IRR (internal rate of return).

Run your program on the following test case:
\begin{verbatim}
  N = 20
  C = 100.0 * arange(3,N+3)
  P = 20000.0
\end{verbatim}

\end{enumerate}


\end{document}

