document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=383490>Question 383490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem: Formulas: y=be^rt; A=P(1+(r/n)^nt <BR>\n" );
document.write( "George has $65 to invest. a. The bank gives him 8.2% continuous interest, how long will it take for George to accrue $100? b. At 7.6% interest compound monthly, how much money will George have in 12 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271527 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=271527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = b * e^rt\r<BR>\n" );
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document.write( "sounds like this is the continuous compounding formula.\r<BR>\n" );
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document.write( "george has $65 to invest.\r<BR>\n" );
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document.write( "at 8.2% continuous interest, how long will it take for george to accrue $100?\r<BR>\n" );
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document.write( "y = $100<BR>\n" );
document.write( "b = $65<BR>\n" );
document.write( "r = .082<BR>\n" );
document.write( "t = time in years\r<BR>\n" );
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document.write( "formula is $100 = $65 * e^(.082*t)\r<BR>\n" );
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document.write( "divide both sides of this formula by 65 to get:\r<BR>\n" );
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document.write( "100/65 = e^(.082*t)\r<BR>\n" );
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document.write( "take log of both sides to get:\r<BR>\n" );
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document.write( "log(100/65) = log(e^(.082*t))\r<BR>\n" );
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document.write( "by laws of logarithms, log(x^y) = y*log(x).\r<BR>\n" );
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document.write( "formula becomes log(100/65) = .082*t * log(e)\r<BR>\n" );
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document.write( "divide both sides of equation by log(e) to get:\r<BR>\n" );
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document.write( "log(100/65) / log(e) = .082*t\r<BR>\n" );
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document.write( "divide both sides of this equation by .082 to get:\r<BR>\n" );
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document.write( "t = (log(100/65) / log(e)) / .082\r<BR>\n" );
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document.write( "log(100/65) = .187086643<BR>\n" );
document.write( "log(e) = log(2.718281828) = .434294482\r<BR>\n" );
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document.write( "log(100/65) / log(e) = .430782916\r<BR>\n" );
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document.write( ".430782916 / .082 = 5.253450196\r<BR>\n" );
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document.write( "you get t = (log(100/65) / log(e)) / .082 =  5.253450196.\r<BR>\n" );
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document.write( "If we did this right, then t = 5.253450196 years\r<BR>\n" );
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document.write( "your original formula is:\r<BR>\n" );
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document.write( "100 = 65 * e^(.082*t)\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "100 = 65 * e^(.082*5.253450196)\r<BR>\n" );
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document.write( "e represents the scientific constant of 2.718281828\r<BR>\n" );
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document.write( "100 = 65 * e^(.082*5.253450196) becomes:\r<BR>\n" );
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document.write( "100 = 65 * 2.718182818^(.082*5.253450196).\r<BR>\n" );
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document.write( "Use your calculator to see that 100 = 100, making t = 5.253450196 correct.\r<BR>\n" );
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document.write( "--------------------------------\r<BR>\n" );
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document.write( "second problem.\r<BR>\n" );
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document.write( "At 7.6% interest compound monthly, how much money will George have in 12 years?\r<BR>\n" );
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document.write( "Formula they show is:\r<BR>\n" );
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document.write( "A=P(1+(r/n)^nt \r<BR>\n" );
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document.write( "A = future value you want to find.<BR>\n" );
document.write( "P = $65.00<BR>\n" );
document.write( "r = .076 / 12 = .006333333<BR>\n" );
document.write( "t = 12 * 12 = 144<BR>\n" );
document.write( "the n they are showing is equal to 12.<BR>\n" );
document.write( "to compound monthly you take the number of years and multiply by 12 and you take the annual interest rate and divide it by 12.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "A = 65 * (1 + (.076/12))^(12*12)\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "A = 65 * (1.00633333)^144 = 161.3395912.\r<BR>\n" );
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document.write( "In 12 years, george will have that much.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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