document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248957>Question 248957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need someone to tell me where \"m\" come from?\r<BR>\n" );
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document.write( "If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent.\r<BR>\n" );
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document.write( "Compound interest formula:<BR>\n" );
document.write( "A=P(1+(r/m))^(mt)\r<BR>\n" );
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document.write( "P=1,000<BR>\n" );
document.write( "r=0.1<BR>\n" );
document.write( "m=12<BR>\n" );
document.write( "t=10\r<BR>\n" );
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document.write( "A=1,000(1+(0.10/12)^((12)(10))<BR>\n" );
document.write( "A=$2,707.04 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181387 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=181387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m looks like it is months.\r<BR>\n" );
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document.write( "usually you are given the annual interest rate and you have to divide that by the number of months to get the monthly interest rate.\r<BR>\n" );
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document.write( "this assumed the compounding of the interest rate is monthly.\r<BR>\n" );
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document.write( "It could be:\r<BR>\n" );
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document.write( "semi-annually (2)<BR>\n" );
document.write( "quarterly (4)<BR>\n" );
document.write( "monthly (12)\r<BR>\n" );
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document.write( "yours is monthly.\r<BR>\n" );
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document.write( "if the compounding is monthly, then the number of time periods have to be in months.\r<BR>\n" );
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document.write( "if they are specified in years, then you have to multiply them by 12 to get months.\r<BR>\n" );
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document.write( "your formula is:\r<BR>\n" );
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document.write( "If $1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent.<BR>\n" );
document.write( "Compound interest formula:<BR>\n" );
document.write( "A=P(1+(r/m))^(mt)<BR>\n" );
document.write( "P=1,000 ***** money invested in the account today.<BR>\n" );
document.write( "r=0.1 ***** annual interest rate of 10% per year.<BR>\n" );
document.write( "m=12 ***** compounding period is in months and there are 12 months to the year.<BR>\n" );
document.write( "t=10 ***** number of years<BR>\n" );
document.write( "A=1,000(1+(0.10/12)^((12)(10))<BR>\n" );
document.write( "A=$2,707.04\r<BR>\n" );
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document.write( "you take the annual interest rate and divide it by 12 to get the monthly interest rate per time period equal to .000833333333\r<BR>\n" );
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document.write( "you take the number of years and multiply it by the number of months in a year to get the number of time periods equal to 120\r<BR>\n" );
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document.write( "your formula becomes:\r<BR>\n" );
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document.write( "A = 1,000 * (1.00833333^120)\r<BR>\n" );
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document.write( "Your answer of 2707... is correct.\r<BR>\n" );
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document.write( "A more general formula would be:\r<BR>\n" );
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document.write( "F = P * (1+(r/c)^(n*c)) where:\r<BR>\n" );
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document.write( "F = future value<BR>\n" );
document.write( "P = present amount<BR>\n" );
document.write( "r = annual interest rate<BR>\n" );
document.write( "c = number of compounding periods per year<BR>\n" );
document.write( "n = number of years\r<BR>\n" );
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document.write( "this works with all compounding periods, not just months.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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