document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195213>Question 1195213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A debtor owes Ryan the following sums, due without interest: $1000 due at the end of 2 years and $2000 due at the end of 5 years. What equivalent single payment would Ryan be willing to accept at the end of 4 years, if money is worth {8%, m=4} to him? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827962 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=827962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure what you mean by m = 4.<BR>\n" );
document.write( "it could be that the money is compounded 4 times a year.<BR>\n" );
document.write( "i'll do both compounded once a year and compounded 4 times a year to show you what the difference is and how to calculate both ways.<BR>\n" );
document.write( "the formula used is f = p * (1 + r) ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period (years in this example).<BR>\n" );
document.write( "n is the number of time periods (years in this example).\r<BR>\n" );
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document.write( "the easiest way to do this is to get the present value of both existing payments at 2 years and 5 years and then get the future value for the sum of that present value at 4 years.<BR>\n" );
document.write( "the result will be as shown below:\r<BR>\n" );
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document.write( "first calculation:<BR>\n" );
document.write( "1000 = p * 1.08 ^ 2<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 1000 / (1.08 ^ 2) = 857.3388203.\r<BR>\n" );
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document.write( "second calculation:<BR>\n" );
document.write( "2000 = p * 1.08 ^ 5<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 2000 / (1.08 ^ 5) = 1361.166394\r<BR>\n" );
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document.write( "sum of first p and second p = 2218.505214.\r<BR>\n" );
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document.write( "third calculation:<BR>\n" );
document.write( "f = 2218.505214 * 1.08 ^ 4 = 3018.251852.\r<BR>\n" );
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document.write( "payments of 1000 in 2 years and 2000 in 5 years are equivalent to 3018.251852 in 4 years.\r<BR>\n" );
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document.write( "that would be your solution, assuming money is compounded once a year.\r<BR>\n" );
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document.write( "if you compound 4 times a year, then the procedure is the same, except that you would divide the interest rate per year by 4 to get the interest rate per quarterly time period and you would multiply the number of years by 4 to get the number of quarterly time periods.\r<BR>\n" );
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document.write( "your first calculation would become:<BR>\n" );
document.write( "p = 1000 / 1.02 ^ 8 = 853.4903712.\r<BR>\n" );
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document.write( "your second calculation would become:<BR>\n" );
document.write( "p = 2000 / 1.02 ^ 20 = 1345.942666.\r<BR>\n" );
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document.write( "the sum of those present values would become equal to 2199.433037..\r<BR>\n" );
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document.write( "your third calculation would become:<BR>\n" );
document.write( "f = 2199.433037 * 1.02 ^ 16 = 3019.350233.\r<BR>\n" );
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document.write( "note that:\r<BR>\n" );
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document.write( "the present value of something for 2 years and then getting the future value of that present value for 4 years is equivalent to getting the future value of that something for 2 years for an additional 2 years.\r<BR>\n" );
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document.write( "the equivalent calculations are shown below:\r<BR>\n" );
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document.write( "calculation 1:<BR>\n" );
document.write( "p = 2000 / 1.08 ^ 2 = 1714.677641 * 1.08 ^ 4 = 2332.8.\r<BR>\n" );
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document.write( "calculation 2:<BR>\n" );
document.write( "f = 2000 * 1.08 ^ 2 = 2332.8.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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