document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149069>Question 1149069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the time required for an investment of 5000 dollars to grow to 8300 dollars at an interest rate of 7.5 percent per year, compounded quarterly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770392 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=770392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula is f = p * (1 + r) ^  n\r<BR>\n" );
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document.write( "p = 5000<BR>\n" );
document.write( "f = 8300<BR>\n" );
document.write( "r = 7.5 / 100 / 4 = .01875<BR>\n" );
document.write( "n = what you want to find.\r<BR>\n" );
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document.write( "formula becomes 8300 = 5000 * (1 + .01875) ^ n<BR>\n" );
document.write( "divide both sides by 5000 to get 8300/5000 = (1 + .01875) ^ n<BR>\n" );
document.write( "take the log of both sides to get log(8300/5000) = log((1 + .01875) ^ n)<BR>\n" );
document.write( "this becomes log(8300/5000) = n * log(1 + .01875)<BR>\n" );
document.write( "divide both sides of log(1 + .01875) to get log(8300/5000) / (log(1.01875) = n<BR>\n" );
document.write( "solve for n to get n = 27.28289636.\r<BR>\n" );
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document.write( "5000 becomes 8300 in 27.28289636 quarters.<BR>\n" );
document.write( "divide that by 4 to get 6.820724091 years.\r<BR>\n" );
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document.write( "note that a quarterly compound rate of .01875 becomes an effective yearly rate of 1.01875 ^ 4 - 1 = .077135866.\r<BR>\n" );
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document.write( "bring that out 6.820724091 years and you get f = 5000 * (1.077135866) ^ 6.820724091 = 8300.\r<BR>\n" );
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document.write( "to find the quarterly rate, you divide the annual rate by 4.<BR>\n" );
document.write( "to find the effective annual rate, you add 1 to the quarterly rate and raise that to the fourth power and then subtract 1.<BR>\n" );
document.write( "the rate is the percent divided by 100.<BR>\n" );
document.write( "put it all together and you get:<BR>\n" );
document.write( "nominal annual rate = 7.5%<BR>\n" );
document.write( "divide by 100 to get a nominal annual .075.<BR>\n" );
document.write( "effective annual rate = (1 + .075/4) ^ 4 - 1 = .0771358658\r<BR>\n" );
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document.write( "you can use the quarterly rate to find the number of quarters, or you can use the effective annual rate to find the number of years.<BR>\n" );
document.write( "the number of quarters divided by 4 is the number of years.<BR>\n" );
document.write( "both ways will get the same answer if you did it right.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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