document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174220>Question 1174220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investment of $4950 earns 11%/a compounded semi-annually. How long will it take for the investment to grow to $9411? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799607 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "annual interest rate: 11% = 0.11<BR>\n" );
document.write( "periodic interest rate (twice a year): 5.5% = 0.055<BR>\n" );
document.write( "periodic growth factor: 1+0.055 = 1.055<br><BR>\n" );
document.write( "The value after n compounding periods is the initial investment, multiplied by the periodic growth factor n times.<br><BR>\n" );
document.write( "You want to know how long it will take the original $4950 to grow to $9411:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9411+=+4950%281.055%5En%29 ALIGN=MIDDLE  ALT=\"9411+=+4950%281.055%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The variable is in an exponent; so to solve algebraically you need to use logarithms.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.055%5En+=+9411%2F4950 ALIGN=MIDDLE  ALT=\"1.055%5En+=+9411%2F4950\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28%281.055%29%29+=+log%28%289411%2F4950%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28%281.055%29%29+=+log%28%289411%2F4950%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%28%289411%2F4950%29%29%2Flog%28%281.055%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%289411%2F4950%29%29%2Flog%28%281.055%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use a calculator....<br><BR>\n" );
document.write( "Or an easy path to the numerical answer is by graphing the two functions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9411 ALIGN=MIDDLE  ALT=\"9411\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4950%281.055%5En%29 ALIGN=MIDDLE  ALT=\"4950%281.055%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a graphing calculator and find that they intersect at n=12.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C400%2C-2%2C16%2C-2000%2C12000%2C4950%281.055%5Ex%29%2C9411%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C400%2C-2%2C16%2C-2000%2C12000%2C4950%281.055%5Ex%29%2C9411%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then remember that n=12 is the number of compounding periods; since the compounding is twice a year, the length of time required for the investment to grow to $9411 is 12/2 = 6 years.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );