document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=961552>Question 961552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me, please? I know the formula is P=Poe^kt, but I don't how to isolate the variable to find Po?!<BR>\n" );
document.write( "Consider a particular investment bond that pays out 3% annual interest<BR>\n" );
document.write( "compounded continually. If the bond is valued at $10,000 after 10 years,<BR>\n" );
document.write( "how much was it worth at 5 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587547 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39626)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=587547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=pe^(kt), using small p to avoid using subscripts.  Big P is for balance of the bond after any time t.   The formula rendered is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=pe%5E%28kt%29 ALIGN=MIDDLE  ALT=\"P=pe%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Your goal is in part, to isolate p, which you can do multiplying both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"e%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "If p=1, the in 1 year, t=1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1%2Ae%5E%280.03%2A1%29 ALIGN=MIDDLE  ALT=\"P=1%2Ae%5E%280.03%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=e%5E%280.03%29=1.0304 ALIGN=MIDDLE  ALT=\"P=e%5E%280.03%29=1.0304\"   DISABLED_style= \"max-width:90%; height:auto;\" >, reasonably near the expected 3% increase.  The value of constant k is the same as the interest rate of 3% or 0.03=r=k.\r<BR>\n" );
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document.write( "Your description of P=10000 after t=10 means you still want to know the initial investment amount.<BR>\n" );
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document.write( "ln(P)=ln(p)+ln(e^(kt))<BR>\n" );
document.write( "ln(P)=ln(p)+kt*1<BR>\n" );
document.write( "ln(P)-kt=ln(p)<BR>\n" );
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document.write( "those steps seem unnecessary although correct.\r<BR>\n" );
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document.write( "BETTER-----------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pe%5E%28kt%29=P ALIGN=MIDDLE  ALT=\"pe%5E%28kt%29=P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=P%2Fe%5E%28kt%29 ALIGN=MIDDLE  ALT=\"p=P%2Fe%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----you could use a calculator for this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10000%2F%28e%5E%280.03%2A10%29%29 ALIGN=MIDDLE  ALT=\"p=10000%2F%28e%5E%280.03%2A10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10000%2F%28e%5E%280.3%29%29 ALIGN=MIDDLE  ALT=\"p=10000%2F%28e%5E%280.3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=7408.18%29 ALIGN=MIDDLE  ALT=\"highlight%28p=7408.18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the initial investment amount.\r<BR>\n" );
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document.write( "Just 5 years instead of 10 years?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=7408.18%2Ae%5E%280.03%2A5%29 ALIGN=MIDDLE  ALT=\"P=7408.18%2Ae%5E%280.03%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=7408.18%2A1.1618342427 ALIGN=MIDDLE  ALT=\"P=7408.18%2A1.1618342427\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P=8607.08%29 ALIGN=MIDDLE  ALT=\"highlight%28P=8607.08%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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