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{\Large TEST 7

Math 1090 - 2}
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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.
Use correct English sentences where necessary for full credit!
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  You invest \$25000 at 10\% per year annual interest, for 20 years.
\begin{enumerate}
\item  What is the future value if this is simple interest?
\item  What is the future value if you compound quarterly?
\item  What is the future value if you compound continuously?
\end{enumerate}

\item  You have \$5000 to invest, 
and you can get 6\% interest compounded quarterly.
How long do you need to invest this money to have \$20000?

\item  Suppose that you just had a child.
The day that this child is born, you decide to set up a college fund.
At the end of each month you put \$200 in a savings account that 
gets 6\% annual interest, compounded every month.
How much is the college fund worth when the kid is 18 and ready to go to college?

\item 
\begin{enumerate}
\item  Find the sum of the first 87 terms of the arithmetic sequence below
\[
87,81,75,69,\ldots
\]
\item  Find the sum of the first 12 terms of the
geometric sequence below (1 point extra credit for the exact sum, simplified)
\[
125,100,80,64,\ldots
\]
\item  In the sequence below, can you know for sure exactly what the next term is?
If you can, what is it?  If not, what not?
\[
5,7,9,11, \ldots
\]
\end{enumerate}

\item  (EXTRA CREDIT - 1 point)
Find a pattern for the sequence.
Make sure your pattern works and explain the pattern to me, 
or better yet, find a formula for the $n$th term.
\[
1,3,6,11,18,29
\]

\end{enumerate}

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