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\begin{document}

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\noindent
\noindent
\parbox{2in}{\bf Math 1030} 
\hfill {\Large \bf Workshop \#2} \hfill
\parbox{2in}{\bf \hfill Due: July $14^{\mathrm{th}}$, 2016}

\vspace{0.35in}

\noindent {\large\bf Name:} \underline{\hskip 3.0 truein} 


\vspace{0.2in}

\noindent {\bf\large 1.} Everyone can retire a millionaire. S\&P 500 index funds historically have averaged about a 10\% annual return. Suppose that you start making deposits into an index fund earning 10\% compounded monthly when you are 25 years old. How much would you need to deposit each month in order to have \$1,000,000 when you are 65?

  \vspace{0.25in}

 Record the Excel command(s) you used to find your answer:

\vspace{0.5in}

How much would you have saved if you put away \$200 each month (for the same span of time and earning the same 10\% c.m. rate of return)?

\vspace{0.25in}

 Record the Excel command(s) you used to find your answer:

\vspace{0.5in}
 

\noindent {\bf\large 2.} Gilbert is saving up for his walkabout. In 5 years, Gilbert plans on hiking around Australia. He estimates that he will need \$3,000 at the beginning of his walkabout (for travel/airfare). Then he'll need about \$500 per month for living expenses as he wanders the roads and deserts. Suppose that he plans to wander for a whole year and that exactly \$500 will be withdrawn from his account each month (at the beginning of the month). If Gilbert's saving account earns 2\% compounded monthly, how much does he need to deposit each month to hit his target in 5 years?

\vspace{0.25in}

Funds needed in 5 years:  \underline{\hspace*{1.5in}}. \hfill  Monthly deposits: \underline{\hspace*{1.5in}}.

  \vspace{0.1in}
   
 Record the Excel command(s) you used to find your answer:

\vspace{0.5in}

\noindent {\bf\large 3.} Cindy is opening a diner. She estimates that she will be able to afford \$30,000 quarterly payments. 

\begin{enumerate}[(a)]
\item If the bank offers her an 8\% (compounded quarterly) loan for 5 years, how much can she afford to borrow?

  \vspace{0.25in}
   
 Record the Excel command(s) you used to find your answer:

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\item Sam the Weasel has offered Cindy \$400,000 if she makes those \$30,000 quarterly payments to him for 5 years. Cindy says that she'll pass on that deal. Why? What rate is he charging? [Your answer should be of the form: XXX.XXX\%]

  \vspace{0.25in}
   
 Record the Excel command(s) you used to find your answer:

\vspace{0.4in}

\end{enumerate}

\noindent {\bf\large 4.} Carl took out a \$45,000 car loan with a 7.25\% (compounded monthly) interest rate. His car payment was \$896.37.

\begin{enumerate}[(a)]
\item How long was Carl's original loan?

  \vspace{0.25in}
   
 Record the Excel command(s) you used to find your answer:

\vspace{0.4in}

\item Suppose that Carl decided to pay \$1,000 each month instead of his regular payment. How many full payments will Carl have to make? What will Carl's final (partial) payment be?

 \vspace{0.25in}

Number of full payments:  \underline{\hspace*{1.5in}}. \hfill  Final payment: \underline{\hspace*{1.5in}}.

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 Record the Excel command(s) you used to find your answer:

\vspace{0.4in}

\end{enumerate}

\noindent {\bf\large 5.}  The Sadowskis just bought a \$260,000 house. They put 10\% down and took out a 15 year mortgage with a 3.25\% interest rate (compounded monthly). 

\vspace{0.1in}

\begin{enumerate}[(a)]

   \item Loan amount? \underline{\hspace{1.75in}} \hfill
           Monthly payment? \underline{\hspace{1.75in}}
   
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   \item How much interest will they pay during their second year? \underline{\hspace{1.7in}}
   
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   \item Fill out the following table:
   
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   \begin{tabular}{|c|c|c|c|c|c|} \hline
   Month & Beg. Balance & Payment & Interest & Amt. to Principal & End Balance \\ \hline
   45     & \myspace & \myspace & \myspace & \myspace & \myspace \\ \hline
   46     & \myspace & \myspace & \myspace & \myspace & \myspace \\ \hline
   \end{tabular}
   
   \vspace{0.05in}

   \item 5 years into the loan, the Sadowskis decide to refinance their mortgage. They start a new 15 year mortgage at 2.5\% (compounded monthly). What is their new payment?
   
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\hfill \hfill  \underline{\hspace{3in}}
   
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    \item (Back to the original loan.) If the Sadowskis pay \$3,000 a month, how long would it take them to pay off their house? What would their final (partial) payment be?

   \vspace{0.2in}
             
\hfill \hfill  It would take \underline{\hspace{0.5in}} years and \underline{\hspace{0.5in}} months. 
\hfill Their last payment would be \$\underline{\hspace{1.5in}}  

\end{enumerate}


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