document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207320>Question 1207320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much money should be deposited today in an account that earns 7 % compounded semiannually so that it will accumulate to $ 13 comma 000 in three​ years?<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 #845128 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=845128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula you can use for this is:<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "(1 + r) is the growth rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "your interest rate is 7% per year / 2 semi-annual periods per year = 3.5% per semi-annual time period.<BR>\n" );
document.write( "that's the percent.<BR>\n" );
document.write( "the rate is that / 100 = .035 per semi-annual time period.<BR>\n" );
document.write( "the growth rate is 1.035 per semi-annual time period.\r<BR>\n" );
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document.write( "the number of time periods is equal to 2 times the number of years.<BR>\n" );
document.write( "3 * 2 = 6 time periods.\r<BR>\n" );
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document.write( "the formula of f = p * (1 + r) ^ n becomes:\r<BR>\n" );
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document.write( "13,000 = p * 1.035 ^ 6\r<BR>\n" );
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document.write( "solve for p to get p = 13,000 / (1.035 ^ 6) = 10575.50838.\r<BR>\n" );
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document.write( "you could also have used a financial calculator, such as the one found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "here are the results from using that calculator.\r<BR>\n" );
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document.write( "with the calculator, you use the rate percent rather than the rate.\r<BR>\n" );
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document.write( "money that you spend is shown as negative.<BR>\n" );
document.write( "money you receive is shown as posiive.\r<BR>\n" );
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document.write( "since you receive the future value, the preset value is shown as negative because that's what you invested to get back the future value.\r<BR>\n" );
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document.write( "the same rules apply.<BR>\n" );
document.write( "the interest rate per time period is equal to the interest rate per year divided by the number of compounding periods per year (7% / 2 = 3.5%).<BR>\n" );
document.write( "the number of time periods is equal to the number of year times the number of compounding compounding periods per year (3 * 2 = 6).\r<BR>\n" );
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document.write( "7% is your nominal interest rate.<BR>\n" );
document.write( "1.035 ^ 2 = 1.071225 -1 = .071225 * 100 = 7.1225% = the effective annual interest rate.<BR>\n" );
document.write( "13000 / 1.035 ^ 6 is the same result as 13000 / 1.071225 ^ 3.<BR>\n" );
document.write( "the effective annual interest rate take into account compounding.<BR>\n" );
document.write( "the nominal annual interest rate doesn't.\r<BR>\n" );
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