document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194508>Question 1194508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much must be deposited at the end of each month for 3.5 years to accumulate to $1,801.00 at 8%<BR>\n" );
document.write( "compounded monthly?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826725 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "1 year = 12 months<BR>\n" );
document.write( "3.5*1 year = 3.5*12 months<BR>\n" );
document.write( "3.5 years = 42 months\r<BR>\n" );
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document.write( "We want the future value to be $1,801 and have it occur at the 42 month mark.<BR>\n" );
document.write( "The annual interest rate in decimal form is r = 0.08\r<BR>\n" );
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document.write( "Divide by 12 to get the monthly version: r/12 = 0.08/12 = 0.00666666666667<BR>\n" );
document.write( "which is approximate.\r<BR>\n" );
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document.write( "The future value annuity formula to use is this<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1)/i<BR>\n" );
document.write( "This is an ordinary annuity and not \"annuity due\".<BR>\n" );
document.write( "This is because the deposits happen at the end of each month, rather at the beginning.\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "FV = future value = 1801<BR>\n" );
document.write( "P = unknown monthly deposit<BR>\n" );
document.write( "i = 0.00666666666667 approximately<BR>\n" );
document.write( "n = 42 months\r<BR>\n" );
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document.write( "Let's solve for P<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1)/i<BR>\n" );
document.write( "1801 = P*( (1+0.00666666666667)^42 - 1)/0.00666666666667<BR>\n" );
document.write( "1801 = P*48.2851385181578<BR>\n" );
document.write( "P = 1801/48.2851385181578<BR>\n" );
document.write( "P = 37.2992613311594<BR>\n" );
document.write( "P = 37.30\r<BR>\n" );
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document.write( "Answer: <font color=red>$37.30</font><BR>\n" );
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