document.write( "Question 1207414: A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly.
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Algebra.Com's Answer #845387 by ikleyn(52834) $\"\"$ $\"About$

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\n" ); document.write( "A car was purchased for $1500 down and payments of $265 at the end of each month for four years.
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\n" ); document.write( "(b) How much interest will be paid?
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document.write( "The purchase price in this problem is $1500 plus the loaned amount.\r\n" );
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document.write( "About the loan, we know that the payments are $265 at the end of each month \r\n" );
document.write( "for 4 years at the annual interest rate of 9% compounded quarterly.\r\n" );
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document.write( "It is equivalent to (it works as) quarterly payments of  3*265 = 795 dollars \r\n" );
document.write( "at the end of each quarter compounded at effective rate r = 0.09/4 per quarter.\r\n" );
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document.write( "Use the formula for periodic payments for the loan at given conditions.\r\n" );
document.write( "The formula is\r\n" );
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document.write( "    Q = ,    (1)\r\n" );
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document.write( "where L is the loan amount; r =  is the effective interest rate per quarter;\r\n" );
document.write( "n is the number of payments (same as the number of quarters, n = 4*4 = 16); \r\n" );
document.write( "Q is the quarterly payment of $795.\r\n" );
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document.write( "Substitute these values into the formula and get an equation for quarterly payments\r\n" );
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document.write( "    795 = .    (2)\r\n" );
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document.write( "We can calculate the coefficient (the factor in the formula) separately\r\n" );
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document.write( "     = 0.07511663.\r\n" );
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document.write( "Now from (1) we find L\r\n" );
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document.write( "    L =  = 10583.54 dollars (rounded to closest cent).\r\n" );
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document.write( "Thus the purchase price for the car was  $10583.54 + $1500 = $12083.54.\r\n" );
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document.write( "It is the ANSWER to question (a).\r\n" );
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document.write( "The amount paid back for this loan was  16 payments by 795 dollars = 16*795 = 12720 dollars.\r\n" );
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document.write( "The interest paid for the loan is the difference $12720 - $10583.54 = $2136.46\r\n" );
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document.write( "It is the ANSWER to question (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution in the post by @MathLover1 is INCORRECT and IRRELEVANT.\r
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\n" ); document.write( "\n" ); document.write( "It is enough to point that in her solution she combines monthly payments with quarterly rates,
\n" ); document.write( "which is the nonsense out of any elementary logic.\r
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\n" ); document.write( "\n" ); document.write( "Also, she uses the formula for the future value of an annuity, which is IRRELEVANT,
\n" ); document.write( "since in this problem we should use a mathematical model for a loan.\r
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\n" ); document.write( "\n" ); document.write( "Madam does not know the subject, can not distinct an annuity from a loan,
\n" ); document.write( "wrongly uses the annuity formula instead of the loan formula and does not understand
\n" ); document.write( "meaning of parameters in her formula.\r
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\n" ); document.write( "\n" ); document.write( " 179% out.\r
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\n" ); document.write( "\n" ); document.write( "Be aware and ignore her post, for the safety of your mind.\r
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