document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446266>Question 446266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the per annum interest rate r required for an investment with continuous compound interest to yield an effective rate of 5.25%. Express your answer as a percent. Your answer must be correct to three decimal places, as in 10.227% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307367 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=307367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the per annum interest rate r required for an investment with continuous compound interest to yield an effective rate of 5.25%. Express your answer as a percent. Your answer must be correct to three decimal places, as in 10.227%<BR>\n" );
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document.write( "Formula for interest compounded continuously:<BR>\n" );
document.write( "A=Pe^rt, P=$ invested, r=annual interest rate, t=years invested<BR>\n" );
document.write( "For ease of calculation, assume $1 is invested for 1 year; that is, P=1 and t=1<BR>\n" );
document.write( "The formula now becomes A=e^r<BR>\n" );
document.write( "Effective interest rate=(A-P)/P=e^r-1=.0525<BR>\n" );
document.write( "e^r=1+.0525=1.0525<BR>\n" );
document.write( "r lne=ln 1.0525<BR>\n" );
document.write( "r=.05117 or 5.117% (ans) </SPAN>\n" );
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