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\begin{document}
\noindent Name: \rule{7cm}{.2pt} \vspace{.3cm} \hfill Date:  \rule{3.5cm}{.2pt}
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\noindent\hrulefill
\begin{center}
{\bf \Large{MA 162}} \\\vspace{.1cm} Week 13 Recitation Worksheet (Tuesday)
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\vspace{-.3cm}
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\begin{center}
\fbox{\textbf{You must show all work to receive full credit.}}
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\noindent We'll spend the rest of the semester considering the mathematics of finance.  This week's worksheet introduces \BLUE{simple interest} and \BLUE{discounts}.\\\\
It costs money to borrow money.  The cost one pays to borrow money is called \emph{interest}.  The money being borrowed or loaned is called the \emph{principal} or \emph{present value}.  When interest is only paid on the original amount borrowed, it is called \emph{simple interest}.  The interest is charged for the amount of time the money is borrowed.  If an amount $P$ is borrowed for a time $t$ at an interest rate of $r$ per time period, then the interest $I$ that is charged is
\begin{equation*}
I=Prt.
\end{equation*}
The total amount $A$ of the transaction is called the \emph{accumulated value} or the \emph{future value}, and is the sum of the principal and interest:
\begin{equation*}
A=P+I=P+Prt=P(1+rt).
\end{equation*}\vspace{0.5cm}

\begin{enumerate}[ref=\#\arabic*]
%1
\item[1$^*$.] (HW17 \#1) What is the interest if \$600 is borrowed for 6 months at 8\% annual simple interest?\vfill


\setcounter{enumi}{1}
%2
\item (HW17 \#2) Find the amount due if \$400 is borrowed for 4 months at 7\% annual simple interest.\vfill


%3
\item (HW17 \#4) Find the length of the loan in months if \$700 is borrowed with an annual simple interest rate of 8\% and with \$774.67 repaid at the end of the loan.\vfill


\newpage
%4
\item (HW17 \#5) Find the annual simple interest rate of a loan where \$1000 is borrowed and \$1060 is repaid at the end of 13 months.\vfill
\end{enumerate}


\noindent Interest can also work in your favor!
\begin{enumerate}
\setcounter{enumi}{4}
%5
\item[5$^*$.] (HW17 \#3) Charlie wants to buy a \$200 stereo set in 9 weeks. How much should he invest now at 16\% annual simple interest to have the money in 9 weeks?\vfill


\setcounter{enumi}{5}
%6
\item (HW17 \#6) An investment pays simple interest, and doubles in 9 years. What is the annual simple interest rate?\vfill
\end{enumerate}


\newpage
\noindent Banks sometimes deduct the simple interest from the loan amount at the time the loan is made. When this happens, we say the loan has been \emph{discounted}. The interest that is deducted is called the \emph{discount} and the actual amount given to the borrower is called the \emph{proceeds}. The amount the borrower is obligated to repay is called the \emph{maturity value}.  If an amount $M$ is borrowed for a time $t$ at a discount rate of $r$ per time period, then the discount $D$ is
\begin{equation*}
D=Mrt.
\end{equation*}
The proceeds $P$ is given by
\begin{equation*}
P=M-D=M-Mrt=M(1-rt).
\end{equation*}\vspace{0.5cm}

\begin{enumerate}
%7
\item[7$^*$.] (HW17 \#7) What are the proceeds for a discounted loan of \$600 repaid in 9 months at 12.25\% annual simple interest?\vfill


\setcounter{enumi}{7}
%8
\item (HW17 \#8) Consider a discounted loan of \$800, where the proceeds equal \$704. The loan is repaid at the end of 16 months. Find the annual simple discount rate.\vfill\vfill
\end{enumerate}
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