Algebra.Com's Answer #845287 by ikleyn(52799)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "For how many years will Prasad make payments on the $28,000 he borrowed to start his machine shop
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document.write( "if he makes payments of $3400 at the end of every three months and interest is 8.08% compounded semi-annually?
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document.write( " The scheme of payments/compounding is non-standard and it is not totally clear how to it really works.\r
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document.write( " So, in my solution I will make some assumptions, but I am not sure if they are adequate.\r
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document.write( " In any case, I will try.\r
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document.write( "It is equivalent to semi-annual payments on the loan with semi-annual payments of 2*3400 = 6800 dollars,\r\n" );
document.write( "while the loan is compounded semi-annually.\r\n" );
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document.write( "So, use the formula for semi-annual payments for a loan\r\n" );
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document.write( " M =  \r\n" );
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document.write( "where P is the loan amount; r =  is the effective interest rate semi-annually;\r\n" );
document.write( "n is the number of payments (same as the number of semi-annual periods); \r\n" );
document.write( "M is the semi-annual payment of $6800.\r\n" );
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document.write( "In this problem M = 6800; P = $28000; r = .\r\n" );
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document.write( "Substitute these values into the formula and get for semi-annual payments\r\n" );
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document.write( " 6800 =  .\r\n" );
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document.write( "We should find \"n\" from this equation.\r\n" );
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document.write( "Divide both sides by 28000. You will get\r\n" );
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document.write( "  =  ,\r\n" );
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document.write( "or\r\n" );
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document.write( " 0.242857143 = .\r\n" );
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document.write( "It implies, step by step\r\n" );
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document.write( "  =  ,\r\n" );
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document.write( " 6.011315417 = ,\r\n" );
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document.write( "  =  ,\r\n" );
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document.write( " 0.166352941 = ,\r\n" );
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document.write( "  = 1 - 0.166352941,\r\n" );
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document.write( " = 0.833647059,\r\n" );
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document.write( "  =  ,\r\n" );
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document.write( " = 1.199548405.\r\n" );
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document.write( "Take logarithm base 10\r\n" );
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document.write( " n*log(1+0.0808/2) = ln(1.199548405)\r\n" );
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document.write( "and find \"n\"\r\n" );
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document.write( " n =  = 4.59.\r\n" );
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document.write( "From these calculations, I make the conclusion that input data in the problem are incorrect,\r\n" );
document.write( "since they lead to the non-integer number of semi-annual payments.\r\n" );
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