document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213724>Question 213724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall that the formula for compounding interest is A = P(1+ r)t where A is the total accumulated amount in an account with principal P compounded at a annual interest rate r once per year for t years.\r<BR>\n" );
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document.write( "a. How many years will it take for a principal of<BR>\n" );
document.write( "P =1000 to reach an amount of A = 5000 when compounded once a year at an annual interest rate of 6%?\r<BR>\n" );
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document.write( "b. If the interest rate is doubled to 12%, what will the number of years be for the<BR>\n" );
document.write( "principal of P =1000 to reach an amount of A = 5000?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161453 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=161453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"A=P%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000=1000%281%2B0.06%29%5Et ALIGN=MIDDLE  ALT=\"5000=1000%281%2B0.06%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1000 ALIGN=MIDDLE  ALT=\"P=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=5000 ALIGN=MIDDLE  ALT=\"A=5000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.06 ALIGN=MIDDLE  ALT=\"r=0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000=1000%281.06%29%5Et ALIGN=MIDDLE  ALT=\"5000=1000%281.06%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2F1000=%281.06%29%5Et ALIGN=MIDDLE  ALT=\"5000%2F1000=%281.06%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1000.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=%281.06%29%5Et ALIGN=MIDDLE  ALT=\"5=%281.06%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285%29%29=log%2810%2C%281.06%5Et%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285%29%29=log%2810%2C%281.06%5Et%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285%29%29=t%2Alog%2810%2C%281.06%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285%29%29=t%2Alog%2810%2C%281.06%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pull down the exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897=t%2Alog%2810%2C%281.06%29%29 ALIGN=MIDDLE  ALT=\"0.69897=t%2Alog%2810%2C%281.06%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897=t%2A0.02531 ALIGN=MIDDLE  ALT=\"0.69897=t%2A0.02531\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the log on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897%2F0.02531=t ALIGN=MIDDLE  ALT=\"0.69897%2F0.02531=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 0.02531.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=27.61636 ALIGN=MIDDLE  ALT=\"t=27.61636\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide and rearrange the equation.\r<BR>\n" );
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document.write( "So it will take about 27.61 years (a little over 27 and a half years) for $1,000 to become $5,000 at an interest rate of 6%\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"A=P%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000=1000%281%2B0.12%29%5Et ALIGN=MIDDLE  ALT=\"5000=1000%281%2B0.12%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1000 ALIGN=MIDDLE  ALT=\"P=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=5000 ALIGN=MIDDLE  ALT=\"A=5000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.12 ALIGN=MIDDLE  ALT=\"r=0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000=1000%281.12%29%5Et ALIGN=MIDDLE  ALT=\"5000=1000%281.12%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2F1000=%281.12%29%5Et ALIGN=MIDDLE  ALT=\"5000%2F1000=%281.12%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1000.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=%281.12%29%5Et ALIGN=MIDDLE  ALT=\"5=%281.12%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285%29%29=log%2810%2C%281.12%5Et%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285%29%29=log%2810%2C%281.12%5Et%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%285%29%29=t%2Alog%2810%2C%281.12%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%285%29%29=t%2Alog%2810%2C%281.12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pull down the exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897=t%2Alog%2810%2C%281.12%29%29 ALIGN=MIDDLE  ALT=\"0.69897=t%2Alog%2810%2C%281.12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897=t%2A0.04922 ALIGN=MIDDLE  ALT=\"0.69897=t%2A0.04922\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the log on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.69897%2F0.04922=t ALIGN=MIDDLE  ALT=\"0.69897%2F0.04922=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 0.04922.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=14.20093 ALIGN=MIDDLE  ALT=\"t=14.20093\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide and rearrange the equation.\r<BR>\n" );
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document.write( "So it will take about 14.2 years (a little over 14 years) for $1,000 to become $5,000 at an interest rate of 12% </SPAN>\n" );
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