document.write( "Question 1203861: you have 2,000 on a credit card that charge a 18% interest rate if you want to pay off the credit card in 4 years. how much will you need to pay each month \n" ); document.write( "

Algebra.Com's Answer #852256 by ikleyn(52873) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "you have 2,000 on a credit card that charge a 18% interest rate if you want to pay off the credit card in 4 years.
\n" ); document.write( "how much will you need to pay each month
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\n" ); document.write( "\n" ); document.write( "        This my solution goes second after the solution by @Theo.\r
\n" ); document.write( "\n" ); document.write( "        @Theo used an online calculator in his solution.\r
\n" ); document.write( "\n" ); document.write( "        Since this web-site is to teach Math, the expected solution should be mathematical.\r
\n" ); document.write( "\n" ); document.write( "        So, I present here a standard mathematical solution.\r
\n" ); document.write( "\n" ); document.write( "        Calculator can be used as a secondary tool for verification.\r
\n" ); document.write( "\n" ); document.write( "        Then the sequence of steps would be normally educative.\r
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document.write( "This is a standard problem on amortization debt (same as paying back for a loan).\r\n" );
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document.write( "Use the standard formula for the monthly payment 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 =  = 0.015  is the effective interest rate per month;\r\n" );
document.write( "n is the number of payments (same as the number of months); M is the monthly payment.\r\n" );
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document.write( "In this problem  P = $2000;  r =  = 0.015.\r\n" );
document.write( "(We are lucky in this case, since we have a precise decimal value for the effective interest rate).\r\n" );
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document.write( "Substitute these values into the formula and get for monthly payment\r\n" );
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document.write( "    M =  = $58.75.\r\n" );
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document.write( "ANSWER.  The monthly payment is $58.75.\r\n" );
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document.write( "Compare it with the @Theo answer of $58.75.\r\n" );
document.write( "It coincide cent-to-cent with my answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved mathematically.\r
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\n" ); document.write( "\n" ); document.write( "In such calculations, it is important to avoid intermediate rounding.
\n" ); document.write( "Rounding can be done at the end, only.\r
\n" ); document.write( "\n" ); document.write( "Intermediate rounding is PROHIBITED, since it leads to wrong answer.\r
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\n" ); document.write( "\n" ); document.write( "Also, a calculator should provide the necessary precision.\r
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\n" ); document.write( "\n" ); document.write( "I use MS Excel in my computer. It works with 15 decimals in mantissa
\n" ); document.write( "and provides the necessary precision.\r
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\n" ); document.write( "\n" ); document.write( "I simply copy-paste my numerical formula into Excel spreadsheet and get the answer in one click.\r
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\n" ); document.write( "\n" ); document.write( "Many standard online calculators provide the necessary precision.\r
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\n" ); document.write( "\n" ); document.write( "You may use, for example, these free-of-charge online calculators\r
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\n" ); document.write( "\n" ); document.write( "https://www.calculatorsoup.com/calculators/financial/loan-calculator.php\r
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\n" ); document.write( "\n" ); document.write( "https://www.calculator.net/payment-calculator.html\r
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\n" ); document.write( "\n" ); document.write( "They are reliable, have convenient user-friendly interface, have complete instructions and descriptions,
\n" ); document.write( "provide the necessary precision and were checked million times. You may use them to check my/your calculations.\r
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\n" ); document.write( "\n" ); document.write( "There is another (= one more) reason why I produced and placed my solution here.\r
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\n" ); document.write( "\n" ); document.write( "@Theo' posts used visual plots to support his solutions.
\n" ); document.write( "These plots were integral inseparable part of his solutions.
\n" ); document.write( "But some time ago, Theo left this forum and stopped supporting web-site with his plots.
\n" ); document.write( "As a result, you see now some colored spots in his posts, where his plots should be.
\n" ); document.write( "Due to this reason, @Theo's posts lost their educational meaning and value.
\n" ); document.write( "Therefore, I create my posts with my own mathematical solutions
\n" ); document.write( "to replace @Theo' solutions and provide meaningful mathematical content.\r
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