document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204090>Question 1204090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You currently have $6,500 (Present Value) in an account that has an interest rate of 7% per year compounded monthly (12 times per year). You want to withdraw all your money when it reaches $16,250 (Future Value). In how many years will you be able to withdraw all your money? Round your answer to 1 decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840110 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>13.2 years</font>\r<BR>\n" );
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document.write( "Work Shown<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "16250 = 6500*(1+0.07/12)^(12*t)<BR>\n" );
document.write( "16250 = 6500*(1.00583333)^(12*t)<BR>\n" );
document.write( "16250/6500 = (1.00583333)^(12*t)<BR>\n" );
document.write( "2.5 = (1.00583333)^(12*t)<BR>\n" );
document.write( "log(2.5) = log( (1.00583333)^(12*t) )<BR>\n" );
document.write( "log(2.5) = 12*t*log( 1.00583333 )<BR>\n" );
document.write( "t = log(2.5)/( 12*log( 1.00583333 ) )<BR>\n" );
document.write( "t = 13.1280168482517<BR>\n" );
document.write( "t = <font color=red>13.2</font><BR>\n" );
document.write( "I rounded up to the nearest tenth.\r<BR>\n" );
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document.write( "If we tried t = 13.1, then,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "A = 6500*(1+0.07/12)^(12*13.1)<BR>\n" );
document.write( "A = 16,218.262943099<BR>\n" );
document.write( "A = 16,218.26<BR>\n" );
document.write( "We're short of the goal $16,250.<BR>\n" );
document.write( "This is why t = 13.1 doesn't work.\r<BR>\n" );
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document.write( "But if you tried t = <font color=red>13.2</font>, then,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "A = 6500*(1+0.07/12)^(12*13.2)<BR>\n" );
document.write( "A = 16,331.8569055279<BR>\n" );
document.write( "A = 16,331.86<BR>\n" );
document.write( "We have gone over the goal of $16,250.<BR>\n" );
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