document.write( "Question 1196016: If a simple discount rate of 11% is equivalent to a simple interest rate of 14.5%. Then what is the length of time under consideration? \n" ); document.write( "

Algebra.Com's Answer #828712 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "If a simple discount rate of 11% is equivalent to a simple interest rate of 14.5%.
\n" ); document.write( "Then what is the length of time under consideration?
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\n" ); document.write( "\n" ); document.write( " In this problem, the most difficult part is to understand what they want from you.\r
\n" ); document.write( "\n" ); document.write( " I will explain it to you in full details.\r
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document.write( "Let B is the borrowed amount, and let R be the amount which should be returned.\r\n" );
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document.write( "Since the simple discount rate is 11%, we have this equation (the definitionm of the simple discount rate) \r\n" );
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document.write( "     = 0.11,\r\n" );
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document.write( "which gives \r\n" );
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document.write( "    R - B = 0.11*R,  or  B = R - 0.11R,  or  B = 0.89R.    (1)\r\n" );
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document.write( "Next, since the loan is simple interest rate of 14.5%, the amount to return at the end is\r\n" );
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document.write( "    R = B + 0.145*B*t,     (2)\r\n" );
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document.write( "where t is the time in years, which is the unknown quantity in this problem.\r\n" );
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document.write( "Substitute B from equation (1) into equation (2).  You will get\r\n" );
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document.write( "    R = 0.89R + 0.145*(0.89*R)*t.\r\n" );
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document.write( "Cancel the factor R in both sides\r\n" );
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document.write( "    1 = 0.89 + 0.145*0.89*t.\r\n" );
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document.write( "Simplify and find t\r\n" );
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document.write( "    1 - 0.89 = 0.12905*t,  or  0.11 = 0.12905*t,  or  t =  = 0.852383 of an year, \r\n" );
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document.write( "which is 0.852383*365 = 311.11 days,  which we should round to 311 days.\r\n" );
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document.write( "ANSWER.  The length of the time under consideration is 311 days (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The \"solution\" by @josgarithmetic is incorrect, illogical and irrelevant.\r
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\n" ); document.write( "\n" ); document.write( "You better ignore it, for the safety of your mind.\r
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