document.write( "Question 1153270: What interest rate compounded monthly will yield an effective interest rate of 8%? \n" ); document.write( "

Algebra.Com's Answer #775466 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "The problem asks which NOMINAL annual interest compounded monthly is equivalent to the annual interest of 8% compounded annually.\r\n" );
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document.write( "Let x be the nominal interest rate  under the question.\r\n" );
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document.write( "Then the account grows from month to month with the effective growing coefficient .\r\n" );
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document.write( "Thus the equation to find x is THIS\r\n" );
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document.write( "     = 1 + 0.08,   or\r\n" );
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document.write( "     = 1.08.\r\n" );
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document.write( "From the equation\r\n" );
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document.write( "     = 1.08^(1/12) = 1.006434.\r\n" );
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document.write( "and finally you get\r\n" );
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document.write( "     = 1.006434 - 1 = 0.006434.\r\n" );
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document.write( "Therefore,  x = 12*0.006434 = 0.0772.\r\n" );
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document.write( "Thus the equivalent (or effective) nominal annual interest rate is 7.72%.\r\n" );
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document.write( "ANSWER.  NOMINAL annual interest compounded monthly, equivalent to the annual interest of 8% compounded annually, is 7.72%.\r\n" );
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document.write( "         Or, in more compact form,  8% annual interest compound annually, is equivalent to 7.72% annual interest compound monthly.\r\n" );
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