document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188488>Question 1188488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Discuss the importance of the number of times interest is compounded annually when borrowing from the bank </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819580 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=819580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the growth factor per year is equal to (1 + r/c) ^ n * x\r<BR>\n" );
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document.write( "r is the nominal growth rate per year (not compounded).<BR>\n" );
document.write( "c is the number of compounding periods per year.\r<BR>\n" );
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document.write( "as an example, assume the nominal growth rate per year is 24%.\r<BR>\n" );
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document.write( "wen you compound only 1 time per year, the growth factor per year becomes (1 + .24/1) ^ (1*1) = 1.24.\r<BR>\n" );
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document.write( "the effective interest rate per year = (1.24 - 1) * 100 = 24%.\r<BR>\n" );
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document.write( "when you compound 4 times a year, the growth factor per year becomes (1 + .24/4) ^ (4 * 1) = 1.26247696.\r<BR>\n" );
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document.write( "the effective interest rate per year becomes (1.26247696 - 1) * 100 = 26.247696%.\r<BR>\n" );
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document.write( "when you compound 12 times a year, the growth factor per year becomes (1 + .24/12) ^ 12 = 1.268241795.\r<BR>\n" );
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document.write( "the effective interest rate per year becomes (1.268241795 - 1) * 100 = 26.8241795%.\r<BR>\n" );
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document.write( "the effective interest rate per year gets higher as the number of compounding periods per year gets higher.\r<BR>\n" );
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document.write( "the effect of this becomes greater as the number of years of inveetment gets higher.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "you invest 1000 at 24% interest rate per year.\r<BR>\n" );
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document.write( "in 20 years, without compounding, your money is worth 1000 * (1 + .24) ^ 20 = 73,864.14979.\r<BR>\n" );
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document.write( "in 20 years, with monthly compounding, your money is worth 1000 * (1 + .24/12) ^ (20 * 12) = 115,888.7352.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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