document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151908>Question 1151908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> difference between nominal rate and effective interest rate and their respective formulae </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773778 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20855)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Effective interest rate is the one which caters the compounding periods during a payment plan.The nominal interest rate is the periodic interest rate times the number of periods per year. Nominal interest rate is also defined as a stated interest rate.<BR>\n" );
document.write( "A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding. <BR>\n" );
document.write( "For example, a nominal annual interest rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >% based on monthly compounding means a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >% interest rate per month (compounded).\r<BR>\n" );
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document.write( "The effective interest rate is always calculated as if compounded annually. The effective rate is calculated in the following way, where ie is the effective rate,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > the nominal rate (as a decimal, e.g. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >% = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.12 ALIGN=MIDDLE  ALT=\"0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and “<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" >” the number of compounding periods per year (for example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > for monthly compounding):\r<BR>\n" );
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document.write( "Effective Rate = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+Nominal_+Rate+%2F+n%29%5En+-+1 ALIGN=MIDDLE  ALT=\"%281+%2B+Nominal_+Rate+%2F+n%29%5En+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5Be%5D+=+%281+%2B+r%2Fn%29%5En+-+1+ ALIGN=MIDDLE  ALT=\"i%5Be%5D+=+%281+%2B+r%2Fn%29%5En+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The nominal interest rate formula can be calculated as: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+m+%2A%28+%28+1+%2B+i%29%5E%281%2Fm%29+-+1+%29 ALIGN=MIDDLE  ALT=\"r+=+m+%2A%28+%28+1+%2B+i%29%5E%281%2Fm%29+-+1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Significance: \r<BR>\n" );
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document.write( "Effective and nominal interest rates allow banks to use the number that looks<BR>\n" );
document.write( "most advantageous to the consumer. When banks are charging interest, they<BR>\n" );
document.write( "advertise the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nominal+ ALIGN=MIDDLE  ALT=\"nominal+\"   DISABLED_style= \"max-width:90%; height:auto;\" >rate, which is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+lower ALIGN=MIDDLE  ALT=\"+lower\"   DISABLED_style= \"max-width:90%; height:auto;\" > and does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+reflect ALIGN=MIDDLE  ALT=\"+reflect\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=how ALIGN=MIDDLE  ALT=\"how\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+much ALIGN=MIDDLE  ALT=\"+much\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interest ALIGN=MIDDLE  ALT=\"interest\"   DISABLED_style= \"max-width:90%; height:auto;\" > the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+consumer ALIGN=MIDDLE  ALT=\"+consumer\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+would ALIGN=MIDDLE  ALT=\"+would\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+owe ALIGN=MIDDLE  ALT=\"+owe\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the balance after a full year of compounding. On the other hand, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=with+ ALIGN=MIDDLE  ALT=\"with+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=deposit+ ALIGN=MIDDLE  ALT=\"deposit+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=accounts ALIGN=MIDDLE  ALT=\"accounts\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+where+ ALIGN=MIDDLE  ALT=\"+where+\"   DISABLED_style= \"max-width:90%; height:auto;\" >banks are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=paying+ ALIGN=MIDDLE  ALT=\"paying+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+interest ALIGN=MIDDLE  ALT=\"+interest\"   DISABLED_style= \"max-width:90%; height:auto;\" >, they <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=generally ALIGN=MIDDLE  ALT=\"generally\"   DISABLED_style= \"max-width:90%; height:auto;\" > advertise the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+effective+ ALIGN=MIDDLE  ALT=\"+effective+\"   DISABLED_style= \"max-width:90%; height:auto;\" >rate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=because ALIGN=MIDDLE  ALT=\"because\"   DISABLED_style= \"max-width:90%; height:auto;\" > it<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+is ALIGN=MIDDLE  ALT=\"+is\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+higher ALIGN=MIDDLE  ALT=\"+higher\"   DISABLED_style= \"max-width:90%; height:auto;\" > than the<BR>\n" );
document.write( "nominal rate. <BR>\n" );
document.write( "Therefore, if you were to borrow money at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8 ALIGN=MIDDLE  ALT=\"+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > percent APR and immediately deposit it in an account at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > percent APY, the deposit account will<BR>\n" );
document.write( "have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=less+ ALIGN=MIDDLE  ALT=\"less+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=money+ ALIGN=MIDDLE  ALT=\"money+\"   DISABLED_style= \"max-width:90%; height:auto;\" >at the end of the year <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=than ALIGN=MIDDLE  ALT=\"than\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+you ALIGN=MIDDLE  ALT=\"+you\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+owe ALIGN=MIDDLE  ALT=\"+owe\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=debt ALIGN=MIDDLE  ALT=\"debt\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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