document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112944>Question 1112944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hellen needs 20 000 in three years time.what is the least amount that she should deposit now into an account that offers an annual interest rate of 15%,compounded every 3 months,to have the required amount by then? The answer to the nearest rand is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727990 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=727990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f = future value<BR>\n" );
document.write( "p = present value<BR>\n" );
document.write( "r = interest rate per time period<BR>\n" );
document.write( "n = number of time periods.\r<BR>\n" );
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document.write( "in your problem.\r<BR>\n" );
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document.write( "f = 20,000<BR>\n" );
document.write( "r = 15% per year compounded quarterly (every 3 months)<BR>\n" );
document.write( "n = 3 years.\r<BR>\n" );
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document.write( "use interest rate as a decimal rather than percent.<BR>\n" );
document.write( "15% = .15<BR>\n" );
document.write( "divide interest rate by number of compounding periods per year to get:<BR>\n" );
document.write( "r = .15/4 = .0375 per quarter.\r<BR>\n" );
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document.write( "multiply number of years by 4 to get number of quarters.<BR>\n" );
document.write( "3 * 4 = 12 quarters.\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n becomes:\r<BR>\n" );
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document.write( "20,000 = p * (1 + .0375) ^ 12\r<BR>\n" );
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document.write( "solve for p to get:\r<BR>\n" );
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document.write( "p = (20,000 / (1 + .0375) ^ 12).\r<BR>\n" );
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document.write( "this results in p = 12,857.97956\r<BR>\n" );
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document.write( "that's how much needs to be invested today in order to have 20,000 in 3 years at 15% per year compounded quarterly.\r<BR>\n" );
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document.write( "12,857.97956 * (1 + .0375) ^ 12 = 20,000\r<BR>\n" );
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document.write( " </SPAN>\n" );
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