document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203599>Question 1203599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula for an investment worth with interest compounded annually is A=P(1+i)^n, where P represents the initial investment, i is the interest rate, and A is the worth of the investment after n years.\r<BR>\n" );
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document.write( "a) Rearrange the formula for P. What was the initial investment of an investment worth $1000 that compounded 10% interest for 10 years?<BR>\n" );
document.write( "b) Rearrange the formula for i. What is the interest rate of an investment whose worth went from $1000 to $1200 in 2 years?<BR>\n" );
document.write( "c) Explain a method with which you could estimate how many years it would take for an investment to reach a certain worth at a certain interest rate.<BR>\n" );
document.write( "d) Estimate how many years would it take an investment of $2100 at 20% interest to reach a worth of $5225?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839293 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " The formula for an investment worth with interest compounded annually is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Bi%29%5En ALIGN=MIDDLE  ALT=\"A=P%281%2Bi%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P ALIGN=MIDDLE  ALT=\"+P\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the initial investment,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i+ ALIGN=MIDDLE  ALT=\"+i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the interest rate, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the worth of the investment after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.\r<BR>\n" );
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document.write( "a) Rearrange the formula for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P ALIGN=MIDDLE  ALT=\"+P\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What was the initial investment of an investment worth $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > that compounded <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >% interest for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10 ALIGN=MIDDLE  ALT=\"+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > years?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Bi%29%5En ALIGN=MIDDLE  ALT=\"A=P%281%2Bi%29%5En\"   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=P=A%2F%281%2Bi%29%5En ALIGN=MIDDLE  ALT=\"P=A%2F%281%2Bi%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1000 ALIGN=MIDDLE  ALT=\"A=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=10 ALIGN=MIDDLE  ALT=\"i=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >%=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10 ALIGN=MIDDLE  ALT=\"0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   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=P=1000%2F%281%2B0.10%29%5E10 ALIGN=MIDDLE  ALT=\"P=1000%2F%281%2B0.10%29%5E10\"   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=P=385.54 ALIGN=MIDDLE  ALT=\"P=385.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) Rearrange the formula for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i ALIGN=MIDDLE  ALT=\"+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What is the interest rate of an investment whose worth went from $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200 ALIGN=MIDDLE  ALT=\"1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ ALIGN=MIDDLE  ALT=\"2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >years?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=P%281%2Bi%29%5En ALIGN=MIDDLE  ALT=\"A=P%281%2Bi%29%5En\"   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=A%2FP=%281%2Bi%29%5En ALIGN=MIDDLE  ALT=\"A%2FP=%281%2Bi%29%5En\"   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=root%28n%2CA%2FP%29=1%2Bi ALIGN=MIDDLE  ALT=\"root%28n%2CA%2FP%29=1%2Bi\"   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=+i=root%28n%2CA%2FP%29-1 ALIGN=MIDDLE  ALT=\"+i=root%28n%2CA%2FP%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if\r<BR>\n" );
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document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1200 ALIGN=MIDDLE  ALT=\"A=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=2 ALIGN=MIDDLE  ALT=\"n+=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i=root%282%2C1200%2F1000%29-1 ALIGN=MIDDLE  ALT=\"+i=root%282%2C1200%2F1000%29-1\"   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=+i=root%282%2C12%2F10%29-1 ALIGN=MIDDLE  ALT=\"+i=root%282%2C12%2F10%29-1\"   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=+i=root%282%2C6%2F5%29-1 ALIGN=MIDDLE  ALT=\"+i=root%282%2C6%2F5%29-1\"   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=+i=1.096-1 ALIGN=MIDDLE  ALT=\"+i=1.096-1\"   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=+i=0.095445 ALIGN=MIDDLE  ALT=\"+i=0.095445\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=9.5445 ALIGN=MIDDLE  ALT=\"i=9.5445\"   DISABLED_style= \"max-width:90%; height:auto;\" >%\r<BR>\n" );
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document.write( "c) Explain a method with which you could estimate how many years it would take for an investment to reach a certain worth at a certain interest rate.\r<BR>\n" );
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document.write( "The Rule of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a calculation that estimates the number of years it takes to double your money at a specified rate of return. \r<BR>\n" );
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document.write( "for example\r<BR>\n" );
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document.write( " $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >% will double to $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+ ALIGN=MIDDLE  ALT=\"200+\"   DISABLED_style= \"max-width:90%; height:auto;\" >in: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2F10=7.2 ALIGN=MIDDLE  ALT=\"72%2F10=7.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "d) Estimate how many years would it take an investment of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2100 ALIGN=MIDDLE  ALT=\"2100\"   DISABLED_style= \"max-width:90%; height:auto;\" > at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20 ALIGN=MIDDLE  ALT=\"+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >% interest to reach a worth of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5225 ALIGN=MIDDLE  ALT=\"5225\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "Note: We don't have to \"estimate\" but will solve it exactly!!!\r<BR>\n" );
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document.write( "to  reach a worth of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5225+ ALIGN=MIDDLE  ALT=\"5225+\"   DISABLED_style= \"max-width:90%; height:auto;\" >will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5225=2100%281%2B0.20%29%5En ALIGN=MIDDLE  ALT=\"5225=2100%281%2B0.20%29%5En\"   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=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9995+ ALIGN=MIDDLE  ALT=\"4.9995+\"   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=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ ALIGN=MIDDLE  ALT=\"5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >years\r<BR>\n" );
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