document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274084>Question 274084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lucy invests $300 at the beginning of each month.  Raymundo invests $4000 at the end of each year and Elise a single amount of $27000 (interest compounded continuously).\r<BR>\n" );
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document.write( "If the interest rate is 10.5% per year, how much will each of them have after 15 years. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200082 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=200082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The annual interest rate is 10.5% / 100% = .095 per year.\r<BR>\n" );
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document.write( "Lucy invests $300 at the beginning of each month.\r<BR>\n" );
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document.write( "Her compounding period is monthly.\r<BR>\n" );
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document.write( "There are 12 compounding periods in the year.\r<BR>\n" );
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document.write( "Interest rate per compounding period is .095 / 12 = .0079166666666\r<BR>\n" );
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document.write( "Number of time periods is equal to number of year times number of compounding periods per year which equals 12 * 15 = 180 time period.\r<BR>\n" );
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document.write( "Future value of payments made at the end of each time period for 180 time periods with monthly compounding equals $118,784.5884\r<BR>\n" );
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document.write( "Adjust for future value of payments made at the beginning of each time period by multiplying these results by 1 + the interest rate period results in:\r<BR>\n" );
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document.write( "$118,784.5884 * 1.0079166666666 = $119,724.9664\r<BR>\n" );
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document.write( "Lucy will have $119,724.9664 at the end of the 15 years.\r<BR>\n" );
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document.write( "Raymundo invests $4000 at the end of each year.\r<BR>\n" );
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document.write( "The compounding periods are once per year so the interest rate for Raymundo is .095 per year and the number of time periods is 15.\r<BR>\n" );
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document.write( "Raymundo will have $122,160.9229 at the end of the 15 years.\r<BR>\n" );
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document.write( "Elise invests $27,000 for 15 years with continuous compounding.\r<BR>\n" );
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document.write( "The continuous compounding formula is F = P*e^(ry) where r is the annual interest rate and y is the number of year.\r<BR>\n" );
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document.write( "Annual interest rate is .095 and the number of years is 15.\r<BR>\n" );
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document.write( "Elise will have $27,000*e^(.095*15) = $112,262.1618 at the end of the 15 years.\r<BR>\n" );
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document.write( "The following information regarding future value of payments and continuous compounding might might be helpful for you to understand what is going on here.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Finance/FVPMT.lesson\" target = \"_blank\">FUTURE VALUE OF A PAYMENT</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Finance/theo-20090921.lesson\" target = \"_blank\">CONTINUOUS COMPOUNDING</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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