document.write( "Question 1193612: If a loan of ₱60,000 is to be settled by 3,200 monthly payments for 2
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Algebra.Com's Answer #848726 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "If a loan of ₱60,000 is to be settled by 3,200 monthly payments for 2
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\n" ); document.write( "\n" ); document.write( " The solution in the post by the other tutor is WRONG.\r
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document.write( "Write a loan equation\r\n" );
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document.write( "    M = ,\r\n" );
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document.write( "where \r\n" );
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document.write( "M is the monthly payment;\r\n" );
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document.write( "L is the loaned amount;\r\n" );
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document.write( "r is the monthly effective rate as a decimal;\r\n" );
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document.write( "n is the number of payments (= the number of months).\r\n" );
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document.write( "In our case this equation takes the form\r\n" );
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document.write( "    3200 = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    0.053333333 = .\r\n" );
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document.write( "In this equation, r is the unknown.\r\n" );
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document.write( "Such equation is unsolvable algebraically, so use the numerical methods.\r\n" );
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document.write( "You may use any of numerous online calculators.\r\n" );
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document.write( "I used DESMOS at  www.desmos.com/calculator\r\n" );
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document.write( "It gave me  r = 0.02077, approximately.\r\n" );
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document.write( "    Here is the link to the DESMOS solution.  \r\n" );
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document.write( "    https://www.desmos.com/calculator/aivq2p1eli\r\n" );
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document.write( "    Click on the intersection point to get its coordinates.\r\n" );
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document.write( "This value  r = 0.02077  is the monthly effective rate - - - so, the annual nominal rate is 12 times this value\r\n" );
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document.write( "     = 12*0.02077 = 0.24924,  or about 0.25,\r\n" );
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document.write( "which corresponds to 25%.\r\n" );
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document.write( "ANSWER. In this problem, the annual interest rate is about 25% compounded monthly.\r\n" );
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document.write( "        Surely, from the usual common sense, this rate is extremely high,\r\n" );
document.write( "        but it tells only that this problem is Math - - - not from real life.\r\n" );
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document.write( "To check my solution, I substituted this value r= 0.02077\r\n" );
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document.write( "into the loan function  f(r) =  = .\r\n" );
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document.write( "It returns the value 0.053333396, which is quite close to  0.053333333, so my solution is confirmed.\r\n" );
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document.write( "To check the solution from the other tutor, I substituted his value r= 0.01\r\n" );
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document.write( "into the loan function  f(r) =  = .\r\n" );
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document.write( "It returns the value 0.047073, which is not close to   = 0.053333333.\r\n" );
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document.write( "So, the other's tutor solution is wrong, which is confirmed.\r\n" );
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