document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81460>Question 81460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much must you deposit in an account that pays 6% annual interest compounded yearly to have a balance of $ 1000 after 10 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58477 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The  equation that is used to solve this problem is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+C%281+%2B+%28r%2Fn%29%29%5E%28n%2At%29 ALIGN=MIDDLE  ALT=\"P+=+C%281+%2B+%28r%2Fn%29%29%5E%28n%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which the variables are:<BR>\n" );
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document.write( "P is the future value of the invested money<BR>\n" );
document.write( "C is the initial deposit<BR>\n" );
document.write( "r is the interest rate expressed as a decimal<BR>\n" );
document.write( "n is the number of times a year that the interest is compounded<BR>\n" );
document.write( "t is the number of years of the investment<BR>\n" );
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document.write( "For this problem the variables are given as follows:<BR>\n" );
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document.write( "P is $1000<BR>\n" );
document.write( "C is the amount of the initial deposit and you are to find C<BR>\n" );
document.write( "r is 0.06 (the interest rate)<BR>\n" );
document.write( "n is 1 compounding per year<BR>\n" );
document.write( "t is 10 years<BR>\n" );
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document.write( "Substituting these values into the equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+C%281+%2B+%280.06%2F1%29%29%5E%281%2A10%29 ALIGN=MIDDLE  ALT=\"1000+=+C%281+%2B+%280.06%2F1%29%29%5E%281%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+C%281+%2B+0.06%29%5E10 ALIGN=MIDDLE  ALT=\"1000+=+C%281+%2B+0.06%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this further simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+C%281.06%29%5E10 ALIGN=MIDDLE  ALT=\"1000+=+C%281.06%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time.  Use your calculator to raise 1.06 to the 10th power. Your calculator<BR>\n" );
document.write( "may have a key for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Ey ALIGN=MIDDLE  ALT=\"x%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If it does, enter 1.06 then press the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Ey ALIGN=MIDDLE  ALT=\"x%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > key, and<BR>\n" );
document.write( "next enter 10 and then press the = key.  You should get 1.790847697. You can also get<BR>\n" );
document.write( "this by entering 1.06 on your calculator and then multiplying it 9 times by 1.06.<BR>\n" );
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document.write( "Substitute 1.790847697 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.06%29%5E10 ALIGN=MIDDLE  ALT=\"%281.06%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+C%2A1.790847697 ALIGN=MIDDLE  ALT=\"1000+=+C%2A1.790847697\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally solve for C by dividing both sides by 1.790847697 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F1.790847697+=+C ALIGN=MIDDLE  ALT=\"1000%2F1.790847697+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "After doing the division on the left side the equation simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=558.3947768+=+C ALIGN=MIDDLE  ALT=\"558.3947768+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rounding this off to the next greatest cent tells you that to end up with at least $1000 <BR>\n" );
document.write( "you need to invest $558.40 at 6% interest compounded yearly for 10 years.<BR>\n" );
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document.write( "(Note that if you invest $558.39 under the same circumstances you end up with $999.99 to the<BR>\n" );
document.write( "nearest cent but by investing $558.40 you get $1000.01 to the nearest cent.)<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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