document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6356>Question 6356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A=$6000 P= $1000 interest is 12% compounded quarterly Find # of interest periods </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3407 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1810)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A=$6000 P= $1000 interest is 12% compounded quarterly<BR>\n" );
document.write( "Find # of interest periods<BR>\n" );
document.write( "`<font face = \"courier new\" color = \"blue\"><b><BR>\n" );
document.write( "The formula is <BR>\n" );
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document.write( "A = P(1+r/n)<sup>nt</sup><BR>\n" );
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document.write( "Where<BR>\n" );
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document.write( "A = ending amount = 6000<BR>\n" );
document.write( "P = beginning amount = 1000<BR>\n" );
document.write( "r = annual rate expressed as a decimal = .12<BR>\n" );
document.write( "n = number of interest periods per year = 4<BR>\n" );
document.write( "` ` (since it's quarterly)<BR>\n" );
document.write( "t = number of years  (which we find first)<BR>\n" );
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document.write( "A = P(1+r/n)<sup>nt</sup><BR>\n" );
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document.write( "Taking logs of both sides<BR>\n" );
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document.write( "logA = log[P(1+r/n)<sup>nt</sup>]<BR>\n" );
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document.write( "logA = logP + log(1+r/n)<sup>nt</sup><BR>\n" );
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document.write( "logA = logP + nt[log(1+r/n)]<BR>\n" );
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document.write( "logP + nt[log(1+r/n)] = logA <BR>\n" );
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document.write( "nt[log(1+r/n)] = logA - logP<BR>\n" );
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document.write( "nt[log(1+r/n)] `` logA - logP<BR>\n" );
document.write( "-------------- = -------------<BR>\n" );
document.write( "`n[log(1+r/n)] ` n[log(1+r/n)] <BR>\n" );
document.write( "`<BR>\n" );
document.write( "nt[log(1+r/n)] `` logA - logP<BR>\n" );
document.write( "-------------- = -------------<BR>\n" );
document.write( "`n[log(1+r/n)] ` n[log(1+r/n)]<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` ` ` ` ` ` ``` logA - logP<BR>\n" );
document.write( "` ` ` ` ` ` `t = -------------<BR>\n" );
document.write( "` ` ` ` ` ` ` `` n[log(1+r/n)]<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` ` ` ` ` ` ``` log6000 - log1000<BR>\n" );
document.write( "` ` ` ` ` ` `t = --------------------<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` `4[log(1+.12/4)]<BR>\n" );
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document.write( "` ` ` ` ` ` ` ``` 3.77815125 - 3<BR>\n" );
document.write( "` ` ` ` ` ` `t = --------------------<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` `4[log(1.03)]<BR>\n" );
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document.write( "` ` ` ` ` ` ` `` ` .7781512504 <BR>\n" );
document.write( "` ` ` ` ` ` `t = ---------------<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` `.0513488988<BR>\n" );
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document.write( "` ` ` ` ` ` ` `` ` .77815125 <BR>\n" );
document.write( "` ` ` ` ` ` `t = ---------------<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` `.0513488988<BR>\n" );
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document.write( "` ` ` ` ` ` `t =  15.15419548 years<BR>\n" );
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document.write( "Multiply by 4 to get the number of interest periods<BR>\n" );
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document.write( "Answer = 60.61678192 which means that 60 interest periods will<BR>\n" );
document.write( "yield slightly less that $6000, or $5891.60 and 61 interest period<BR>\n" );
document.write( "will yield slightly more than $6000, or $6068.40.<BR>\n" );
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document.write( "Edwin <font face = \"wingdings\" color = \"red\" size = 7>J</font></b>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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