document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206511>Question 1206511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You make semiannual deposits of $398<BR>\n" );
document.write( " into an ordinary annuity earning 6.8%<BR>\n" );
document.write( " compounded semiannually.<BR>\n" );
document.write( "How much money is in the account after 11<BR>\n" );
document.write( " years? \r<BR>\n" );
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document.write( "How much interest did you earn in your first year?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844045 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52776)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "You make semiannual deposits of $398 into an ordinary annuity earning 6.8% compounded semiannually. <BR>\n" );
document.write( "(a) How much money is in the account after 11 years?<BR>\n" );
document.write( "(b) How much interest did you earn in your first year?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "It is a classic Ordinary Annuity saving plan (deposits are made at the end \r\n" );
document.write( "of each semiannual period).  The general formula is \r\n" );
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document.write( "    FV = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29 ALIGN=MIDDLE  ALT=\"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,    (1)\r\n" );
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document.write( "where  FV is the future value of the account;  P is the semiannual payment (deposit); \r\n" );
document.write( "r is the nominal semiannual percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 2, in this case).\r\n" );
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document.write( "Under the given conditions, P = 398;  r = 0.068/2 0.034;  n = 2*11 = 22.  \r\n" );
document.write( "So, according to the formula (1), the account after 11 years will be\r\n" );
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document.write( "    FV = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=398%2A%28%28%281%2B0.034%29%5E22-1%29%2F0.034%29 ALIGN=MIDDLE  ALT=\"398%2A%28%28%281%2B0.034%29%5E22-1%29%2F0.034%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=398%2A%28%281.034%5E22-1%29%2F0.034%29 ALIGN=MIDDLE  ALT=\"398%2A%28%281.034%5E22-1%29%2F0.034%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $12,720.32.    <U>Answer to (a)</U>\r\n" );
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document.write( "The interest earned in the first year is \r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=398%2A%28%28%281%2B0.034%29%5E2-1%29%2F0.034%29-2%2A398 ALIGN=MIDDLE  ALT=\"398%2A%28%28%281%2B0.034%29%5E2-1%29%2F0.034%29-2%2A398\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 13.53 dollars.    <U>ANSWER to (b)</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On Ordinary Annuity saving plans, &nbsp;see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.\r<BR>\n" );
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document.write( "When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.\r<BR>\n" );
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document.write( "To make such complicated calculations as they are in this problem,<BR>\n" );
document.write( "you should have/use an appropriate calculator for such long formulas.\r<BR>\n" );
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document.write( "Ideal choice is MS Excel, if you have it in your computer.\r<BR>\n" );
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document.write( "Then you write a formula in a text editor, copy-paste it <BR>\n" );
document.write( "into an Excel work-sheet cell and click \"enter\" - the result is ready <BR>\n" );
document.write( "in the next second.\r<BR>\n" );
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document.write( "If you have no MS Excel in your computer, you may find similar <BR>\n" );
document.write( "free of charge calculators in the Internet. One such calculator is\r<BR>\n" );
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document.write( "www.desmos.com/calculator\r<BR>\n" );
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document.write( "It allows you to do the same thing: you write a formula in a text editor, <BR>\n" );
document.write( "copy-paste it into this calculator and click \"enter\" - the result is ready <BR>\n" );
document.write( "in the next second.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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