document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179712>Question 1179712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate, to the nearest cent, the present value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. <BR>\n" );
document.write( "6 years, at 4.1% per year, compounded weekly (52 times per year)<BR>\n" );
document.write( "PV = $  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809302 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=809302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there is a formula to handle this, but there is also a calculator that makes the job easier.\r<BR>\n" );
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document.write( "using the online calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a>, i get:\r<BR>\n" );
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document.write( "present value = 782.00 rounded to the nearest penny.\r<BR>\n" );
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document.write( "i confirmed using my own calculator that the answer is 781.9980202.\r<BR>\n" );
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document.write( "round that to the nearest penny to get 782.\r<BR>\n" );
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document.write( "both calculator agree.\r<BR>\n" );
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document.write( "the formula you can use for this is:\r<BR>\n" );
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document.write( "PRESENT VALUE OF A FUTURE AMOUNT\r<BR>\n" );
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document.write( "p = f/(1+r)^n\r<BR>\n" );
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document.write( "p is the present value.<BR>\n" );
document.write( "f is the future amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "f = 1000<BR>\n" );
document.write( "(1+r) = (1 + 4.1/5200) = .0007884615385<BR>\n" );
document.write( "n = 6 * 52 = 312\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "p = 1000 / 1.0007884615385^312 = 781.9980202\r<BR>\n" );
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document.write( "round to nearest penny to get 782.\r<BR>\n" );
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document.write( "everybody agrees, so the answer is probably correct.\r<BR>\n" );
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document.write( "here are the results from using the online calculator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/050401.jpg\">\r<BR>\n" );
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document.write( "the inputs are everything but pv.\r<BR>\n" );
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document.write( "that's the output.\r<BR>\n" );
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document.write( "what you see is the formatted version of the inputs and outputs.<BR>\n" );
document.write( "the actual inputs were:<BR>\n" );
document.write( "fv = 1000<BR>\n" );
document.write( "np = 312<BR>\n" );
document.write( "ir = .0788461538\r<BR>\n" );
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document.write( "note that the calculator uses percent, while the formula uses rate.\r<BR>\n" );
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document.write( "4.1/52 = .0788461538%\r<BR>\n" );
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document.write( "divide that by 100 to get the rate of .000788461538.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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