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\begin{center}
{\Large TEST 7

Math 1090 - 4}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
Use the back of the pages if necessary.

\vspace{.2in}

Name \rule{5in}{.2pt}

\vspace{.2in}

Formulas:
\[
\begin{array}{|l|c|}
\hline
& \\
\mbox{Future Value} &
	S=P \left(1+\frac{j}{m}\right)^{mt} \\
& \\ \hline & \\
\mbox{Future Value} &
	S=P e^{rt} \\
& \\ \hline & \\
\mbox{FV of Ordinary Annuity} &
	S=R \cdot \left[\frac{(1+i)^n-1}{i}\right] \\
& \\ \hline & \\
\mbox{FV of Annuity Due} &
	S=R \cdot \left[\frac{(1+i)^{n+1}-1}{i}\right] - R \\
& \\ \hline & \\
\mbox{PV of Ordinary Annuity} &
	A_n=R \cdot \left[\frac{1-(1+i)^{-n}}{i}\right] \\
& \\ \hline & \\
\mbox{PV of Deferred Annuity} &
	A_{(n,k)}=R \cdot \left[\frac{1-(1+i)^{-n}}{i} \right] (1+i)^{-k} \\
& \\ \hline & \\
\mbox{Amortization} &
	R=A_n \cdot \left[\frac{i}{1-(1+i)^{-n}}\right] \\
& \\ \hline & \\
\mbox{Sinking Fund} &
	R=S \cdot \left[\frac{i}{(1+i)^{n}-1}\right] \\
& \\ \hline 
\end{array}
\]


\begin{enumerate}

\item  You have \$5000 and you invest it for 10 years at 6\% annual interest.
What is the future value if the interest is
\begin{enumerate}
\item  compounded annually?
\item  compounded monthly?
\item  compounded continuously?
\end{enumerate}


\item  If you compound your 6\% annual interest continuously, and you start with \$5000, 
how long until you have \$8000?

\item  What is better and why?
\begin{enumerate}
\item  13.3\% annual interest compounded biannually,
\item  13\% annual interest compounded continuously,
\item  13.2\% annual interest compounded 6 times a year.
\end{enumerate}

\item  Suppose that when you are 30 you get an inheritance of \$50,000.
You decide that you will shove this money in a bank 
(with 7\% annual interest compounded monthly) for 30 years and then use 
it for your retirement.
How much can you withdraw every month from the time you are 60 until you are 80?
(You withdraw an equal amount each month)

\item  At the birth of your new baby, you start putting some money into an account
at the beginning of every month.  You account pays 8\% annual interest compounded monthly.
How much to you need to deposit every month in order to have \$25,000 when you child is
18 and ready to start college?

\item  Suppose that you just started college.
Rather then pay for your expenses as they came up, your parents dropped a
lump sum of money into an account that pays 5\% annual interest compounded 6 times a year.
You then receive \$800 every 2 months for 4 years.
How much money did your parents have to drop in the account to make this possible?


\item  (EXTRA CREDIT - 6 points)

\textbf{Important:}
You will only get credit if you use the methods taught in class.
Also, decimals are not OK.  To get credit, leave your answer in a fraction.

These points (if any) will be added to this test.

\begin{enumerate}
\item  Find the sum of the first 8 terms of the geometric sequence below.
\[
\frac{2}{3},3, \ldots
\]

\item  You have an arithmetic sequence with 7th term 12 and 82nd term 387.
What is the 193rd term?

\end{enumerate}




\end{enumerate}

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