document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970931>Question 970931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This one has me stumped:\r<BR>\n" );
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document.write( "The owner of a café plans to open a second location in 8 years.  She purchases an annuity that pays 8.5% interest compounded annually.  If the payment is $3,450 a year, find the future value of the annuity in 8 years.  Round your answer to the nearest cent.\r<BR>\n" );
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document.write( "Thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593588 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> annuity pays 8.5% interest compounded annually.<BR>\n" );
document.write( "the payment is 3450 each year.<BR>\n" );
document.write( "find the future value of the annuity in 8 years.\r<BR>\n" );
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document.write( "fv = what you want to find<BR>\n" );
document.write( "pv = 0<BR>\n" );
document.write( "pmt = 3450 each year.<BR>\n" );
document.write( "interest rate percent = 8.5% per year compounded annually.\r<BR>\n" );
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document.write( "the only question is whether she makes the payment at the beginning of each year or at the end of each year.\r<BR>\n" );
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document.write( "without knowing that, we'll do both.\r<BR>\n" );
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document.write( "the formula for the future value of an annuity is in the following link.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.arachnoid.com/lutusp/finance.html\" target = \"_blank\">http://www.arachnoid.com/lutusp/finance.html</a>\r<BR>\n" );
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document.write( "that link also includes a calculator where you can test your results.\r<BR>\n" );
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document.write( "look for the formula for fv = .......\r<BR>\n" );
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document.write( "there are two formulas.\r<BR>\n" );
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document.write( "the one on the left is for payments at the beginning of the time period.\r<BR>\n" );
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document.write( "the one on the right is for payments at the end of the time period.\r<BR>\n" );
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document.write( "the easy way to do it is to use the formula for payments at the end of the time period and then multiply the result by 1 + r.\r<BR>\n" );
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document.write( "this will give you the future value for payments at the beginning of the time period.\r<BR>\n" );
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document.write( "you need to determine what the time periods are and translate the time periods you are given to the number of time periods reqquired.\r<BR>\n" );
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document.write( "the formula is based on compounding periods per year.\r<BR>\n" );
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document.write( "time periods = y*c where y is number of years and c is number of compounding periods per year.\r<BR>\n" );
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document.write( "interesst rate per time period = r / c where r is the interest rate per year and c is the number of compounding periods per year.\r<BR>\n" );
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document.write( "in this problem, the time periods are in years and the interest rate is in years so no adjustment is necessary.\r<BR>\n" );
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document.write( "the calculator uses interest rate percent.\r<BR>\n" );
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document.write( "the formulas use interest rate.\r<BR>\n" );
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document.write( "convert from interest rate percent to interest rate by dividing the interest rate percent by 100.\r<BR>\n" );
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document.write( "8.5% interest rate percent per year is the same as .085 per year interest rate per year.\r<BR>\n" );
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document.write( "i used the calculator and the formulas and got the same answers.\r<BR>\n" );
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document.write( "the calculator results are shown below:\r<BR>\n" );
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document.write( "the first one assumes payments made at the beginning of the year.\r<BR>\n" );
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document.write( "the second one assumes payments made at the end of the year.\r<BR>\n" );
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document.write( "if you take the PMABOY future value number and divide it by the PMAEOY future value number, you will see that BOY is 1.085 * EOY results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/051801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/051802.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "when you usde the calculator to calculate FV, you do the following.\r<BR>\n" );
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document.write( "enter 3450 for present value.<BR>\n" );
document.write( "leave future value blank<BR>\n" );
document.write( "enter 8 for number of payments<BR>\n" );
document.write( "enter 3450 for payment amount<BR>\n" );
document.write( "enter 8.5 for interest rate per period percent.<BR>\n" );
document.write( "select payment at beginning or end of year, whichever you want.<BR>\n" );
document.write( "left click mouse on FV button.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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