document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878985>Question 878985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im sorry I haven't taken a math class in 20 years and I wasn't good to begin with and so I am lost here. I don't want someone to answer for me, I just wanna know how to do it correctly.\r<BR>\n" );
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document.write( "How many years will it take $1000 to grow to 1700 if invested at 6 percent and compounded quarterly? continuously?\r<BR>\n" );
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document.write( "Thankyou </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530433 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=530433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the \"compounded quarterly\" part, use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+PV%2A%281%2Br%2Fn%29%5E%28n%2At%29 ALIGN=MIDDLE  ALT=\"FV+=+PV%2A%281%2Br%2Fn%29%5E%28n%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where,\r<BR>\n" );
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document.write( "FV = future value (amount you will have in the account at some point in the future)<BR>\n" );
document.write( "PV = present value<BR>\n" );
document.write( "r = interest rate (in decimal form)<BR>\n" );
document.write( "n = compounding frequency<BR>\n" );
document.write( "t = time in years\r<BR>\n" );
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document.write( "In this case,\r<BR>\n" );
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document.write( "FV = 1700 (amount you want t years in the future)<BR>\n" );
document.write( "PV = 1000 (amount you deposit right now)<BR>\n" );
document.write( "r = 0.06 (6% = 6/100 = 0.06)<BR>\n" );
document.write( "n = 4 (compounded quarterly means you are compounding 4 times a year)<BR>\n" );
document.write( "t = unknown (you are solving for this) \r<BR>\n" );
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document.write( "Plug all of that info into the equation and solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+PV%2A%281%2Br%2Fn%29%5E%28n%2At%29 ALIGN=MIDDLE  ALT=\"FV+=+PV%2A%281%2Br%2Fn%29%5E%28n%2At%29\"   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=1700+=+1000%2A%281%2B0.06%2F4%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"1700+=+1000%2A%281%2B0.06%2F4%29%5E%284%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given info.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1700%2F1000+=+%281%2B0.06%2F4%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"1700%2F1000+=+%281%2B0.06%2F4%29%5E%284%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1000.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F10+=+%281%2B0.06%2F4%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"17%2F10+=+%281%2B0.06%2F4%29%5E%284%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7+=+%281%2B0.06%2F4%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"1.7+=+%281%2B0.06%2F4%29%5E%284%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F10 ALIGN=MIDDLE  ALT=\"17%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to decimal form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7+=+%281%2B0.015%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"1.7+=+%281%2B0.015%29%5E%284%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06%2F4 ALIGN=MIDDLE  ALT=\"0.06%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.015 ALIGN=MIDDLE  ALT=\"0.015\"   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=1.7+=+%281.015%29%5E%284%2At%29 ALIGN=MIDDLE  ALT=\"1.7+=+%281.015%29%5E%284%2At%29\"   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=log%28%281.7%29%29+=+log%28%28%281.015%29%5E%284%2At%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%281.7%29%29+=+log%28%28%281.015%29%5E%284%2At%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply logs to both sides (so we can isolate that exponent)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%281.7%29%29+=+4t%2Alog%28%281.015%29%29 ALIGN=MIDDLE  ALT=\"log%28%281.7%29%29+=+4t%2Alog%28%281.015%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pull down the exponent (one of the many log rules).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%281.7%29%29%2Flog%28%281.015%29%29+=+4t ALIGN=MIDDLE  ALT=\"log%28%281.7%29%29%2Flog%28%281.015%29%29+=+4t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%281.015%29%29 ALIGN=MIDDLE  ALT=\"log%28%281.015%29%29\"   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=35.6398725055742+=+4t ALIGN=MIDDLE  ALT=\"35.6398725055742+=+4t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator to 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=35.6398725055742%2F4+=+t ALIGN=MIDDLE  ALT=\"35.6398725055742%2F4+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.90996812639356+=+t ALIGN=MIDDLE  ALT=\"8.90996812639356+=+t\"   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=t+=+8.90996812639356 ALIGN=MIDDLE  ALT=\"t+=+8.90996812639356\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation.\r<BR>\n" );
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document.write( "So it takes approximately 8.90996812639356 years. If you must round to a whole number, then round up to get 9 years. You round up to guarantee you let enough time go by to get past the target you want.\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "For the next part, the \"compounded continuously\" part, use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+PV%2Ae%5E%28r%2At%29 ALIGN=MIDDLE  ALT=\"FV+=+PV%2Ae%5E%28r%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where,\r<BR>\n" );
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document.write( "FV = future value (amount you will have in the account at some point in the future)<BR>\n" );
document.write( "PV = present value<BR>\n" );
document.write( "e = 2.718... (it's a constant like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it goes on forever without a known pattern)<BR>\n" );
document.write( "r = interest rate (in decimal form)<BR>\n" );
document.write( "t = time in years\r<BR>\n" );
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document.write( "I'll let you do this part. </SPAN>\n" );
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