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\title{MA162: Finite mathematics}
\subtitle{Financial Mathematics}
\author{Paul Koester}
\institute{University of Kentucky}
\date{February 5, 2014}

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\begin{document}

\maketitle

\begin{frame}[t]{Annuities}
\begin{itemize}
  \item A sequence of regular cash flows of \$R occurs at the end of each period for the next n periods.  (R stands for ``regular cash flow''))
  \item Interest rate is i per period.
  \item Then the present value, P, of this annuity is 
  \[ P = R \cdot \frac{1 - (1+i)^{-n}}{i} \]
  \item In Excel, P can be computed by \emph{=PV(i,n,R)}.
  \item In WeBWorK, P can be computed by \emph{R * PV(i,n)}.
  \item P answers the question ``What is the value of this entire stream of cash flows evaluated at the beginning'' 

\end{itemize}
\end{frame}

\begin{frame}[t]{Annuities}
\begin{itemize}
  \item Then the accumulated value, or future value, F, of this annuity is 
  \[ F = R \cdot \frac{(1 + i)^{n} - 1}{i} \]
  \item In Excel, P can be computed by \emph{=FV(i,n,R)}.
  \item In WeBWorK, P can be computed by \emph{R * FV(i,n)}.
  \item F answers the questions like ``If you save \$R at the end of each year for the next n years and interest is i per year, then what is the 
  value of your savings at the end?''

\end{itemize}
\end{frame}

\begin{frame}{Ex. 1: FV of Annuity}
\begin{itemize}  
  \item Determine the accumulated value of a 8 year annuity with level cash flows of \$1200 at the end of each quarter, 
  provided the cash flows earn \(6\%\) annual interest compounded quarterly.
  \vfill
  % Do simple upper estimate...
  \item Determine the present value of the above annuity.
\end{itemize}
\end{frame}

\begin{frame}{Ex 2: PV of Annuity}
\begin{itemize}  
  \item Orion was involved in a terrible accident at work.  
  \item Worker's Comp insurance is to pay Orion \$45,000 at the end of each year for the next 30 years. 
  \item Orion gets a phone call from one of those companies from day-time TV ads that say they buy ``structured settlements and annuities.''  
    Basically, the company will give Orion a large lump sum of cash today in exchange for his annuity.
  \item The company offers to give him \$550,000 today in exchange for his structured settlement.  
  \item Orion wants to make sure they are not trying to rip him off.  
  \item Assuming interest is 5\% annually compounded, what is the fair value of his structured settlement, 
    and should he take the \$550,000 now?
\end{itemize}
\end{frame}

\begin{frame}{Ex 3: IRA}
\begin{itemize}  
  \item Gilligan is 25 years old.  He just graduated with his MBA and got a good job.
  \item He is going to start saving for retirement.  
   He will do this by depositing \$5000 at the end of each year into an IRA (Individual Retirement Account).
  \item Assuming the account earns 12\% per year compounded annually, how much will Gilligan have in this account when he retires at age 65?
\end{itemize}
\end{frame}

\begin{frame}{Ex 3: IRA}
\begin{itemize}  
  \item Now suppose Gilligan decides to wait until he's 30 to start saving for retirement.  
  \item How much will he have in his retirement account when he turns 65?
\end{itemize}
\end{frame}

\begin{frame}{Ex 4: Myra's early retirement}
\begin{itemize}  
  \item Myra is 40 years old.  She wants to retire early, when she turns 55.  
  \item She currently has \$250,000 in an investment account.
  \item She figures she can deposit \$1000 at the end of each month from now until the time she retires.
  \item Her investment account will earn 12\% interest per year compounded monthly.
  \item When she retires, she will move her investment account to a safer but lower yielding account which will earn 3\% per year compounded monthly.
  \item She figures her retirement funds must last until she turns 85.
  \item How much will she be able to withdraw from the account at the end of each month during her retirement?
\vfill
\end{itemize}
\end{frame}

%\begin{frame}{Ex 4: Morty's Mortgage}
%\begin{itemize}  
%  \item Morty has a home mortgage with some special terms.
%  \item He does have to make any payments for the next 2 years. 
%  \item For the next three years, he has to make monthly payments of \$1800 at the end of each month.
%  \item For the next 20 years, he has to make monthly payments of \$1300 at the end of each month.
%  \item The interest on the loan is 4.8\% per year compounded monthly.
%  \item Determine the principal of the loan.
%\vfill
%\end{itemize}
%\end{frame}

\end{document}

