document.write( "Question 1193609: A second-hand car was bought for ₱100,000 downpayment and
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Algebra.Com's Answer #848693 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A second-hand car was bought for ₱100,000 downpayment and
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\n" ); document.write( "\n" ); document.write( " Calculations in the post by @yurtman are incorrect.\r
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document.write( "To calculate the cash price of the car, we need to find the present value of the monthly installment \r\n" );
document.write( "payments and add the downpayment.\r\n" );
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document.write( "        Step 1: Formula for Present Value of an Annuity\r\n" );
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document.write( "The formula for the present value of an annuity is:\r\n" );
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document.write( "    PV = \r\n" );
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document.write( "Where:  \r\n" );
document.write( "    PV  = present value of the monthly installments (the amount equivalent to these payments today)  \r\n" );
document.write( "    M   = monthly payment (10,000)\r\n" );
document.write( "    r   = monthly interest rate (0.12/12} = 0.01)  \r\n" );
document.write( "    n   = total number of payments (48 = 4*12)  \r\n" );
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document.write( "--\r\n" );
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document.write( "        Step 2: Calculate the Present Value of Installments\r\n" );
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document.write( "Substitute the known values:\r\n" );
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document.write( "    PV =  = 379739.60   <<<---===  about one order more than in the post by @yurtman \r\n" );
document.write( "                                                                 I performed this calculation using my Excel spreadsheet\r\n" );
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document.write( "So:\r\n" );
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document.write( "   PV = 379739.60\r\n" );
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document.write( "        Step 3: Add the Downpayment\r\n" );
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document.write( "The total cash price of the car is:\r\n" );
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document.write( "    Cash Price = Downpayment + PV = 100,000 + 379739.60 = 479739.60\r\n" );
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document.write( "        Final Answer:\r\n" );
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document.write( "The cash price of the car is approximately 479739.60.\r\n" );
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