document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141443>Question 141443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An initial investment is made at 4.5% interest, compounded semi annually, how long will it take to become 4 times the original amount? \r<BR>\n" );
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document.write( "Is this question even possible without the amount of the initial investment? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103074 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An initial investment is made at 4.5% interest, compounded semi annually, how long will it take to become 4 times the original amount? <BR>\n" );
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document.write( "Using the formula; A = P(1+(i/n))^nt<BR>\n" );
document.write( "where<BR>\n" );
document.write( "A = resulting amt<BR>\n" );
document.write( "P = initial amt<BR>\n" );
document.write( "i = interest in decimals<BR>\n" );
document.write( "n = no. of time per year<BR>\n" );
document.write( "t = no. of yrs<BR>\n" );
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document.write( "In this problem we just assign a value of 1 for P and 4 for A:<BR>\n" );
document.write( "It asks how long so we solve for t:<BR>\n" );
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document.write( "1(1 + (.045/2))^2t = 4<BR>\n" );
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document.write( "(1+.0225)^2t = 4<BR>\n" );
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document.write( "(1.0225)^2t = 4<BR>\n" );
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document.write( "log(1.0225^2t) = log(4)<BR>\n" );
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document.write( "Log equiv of exponents<BR>\n" );
document.write( "2t*log(1.0225) = log(4)<BR>\n" );
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document.write( "Find the logs:<BR>\n" );
document.write( "2t*.0096633 = .60206<BR>\n" );
document.write( "2t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.60206%2F.0096633 ALIGN=MIDDLE  ALT=\".60206%2F.0096633\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2t = 62.3 <BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62.3%2F2 ALIGN=MIDDLE  ALT=\"62.3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 31.15 <BR>\n" );
document.write( "So we have to say it will take 31.5 yrs for your money to quadruple at 4.5%, semiannually<BR>\n" );
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document.write( "Check solution on a calc: enter: (1.0225)^(2*31.5) = 4.06 </SPAN>\n" );
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