document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194734>Question 1194734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You would like to have $900,000 when you retire in 35 years. How much should you invest each quarter if you can earn a rate of 5.4% 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 #826997 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=826997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We'll be using a future value of an annuity<BR>\n" );
document.write( "The formula is<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "We'll be using the ordinary annuity and not the \"annuity due\" variation.\r<BR>\n" );
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document.write( "FV = future value<BR>\n" );
document.write( "P = payment per period<BR>\n" );
document.write( "i = interest rate per period (in decimal form)<BR>\n" );
document.write( "n = number of periods\r<BR>\n" );
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document.write( "In this case, each period is one quarter (aka 3 months, since 12/4 = 3).\r<BR>\n" );
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document.write( "We know the following:<BR>\n" );
document.write( "FV = 900,000 = amount we want at a later future date<BR>\n" );
document.write( "i = 0.054/4 = 0.0135 which is exact<BR>\n" );
document.write( "n = 35*4 = 140 quarters\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( "900,000 = P*( (1+0.0135)^140 - 1 )/0.0135<BR>\n" );
document.write( "900,000 = P*410.088990826382<BR>\n" );
document.write( "P = (900,000)/410.088990826382<BR>\n" );
document.write( "P = 2194.64560164462<BR>\n" );
document.write( "P = <font color=red>2194.65</font>\r<BR>\n" );
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document.write( "Answer: You should deposit <font color=red>$2,194.65</font> at the end of each quarter, do so for 140 quarters (aka 35 years), to accumulate $900,000 which is composed of the deposits plus added interest.\r<BR>\n" );
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document.write( "The tutor @Theo offers a great calculator to check your answer. The answer is highlighted in red in their screenshot; however, the payment amount should be a positive number. <BR>\n" );
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