document.write( "Question 1178497: The Trissel family agreed on a price of $223,600 for a home. Their company credit union offers a 5.9% 20 year loan with 15% down, resulting in a monthly payment of $1350.71. Find the monthly payment for the Trissels if they choose a 15 year loan instead of 20 with the same APR and down payment. How much would they save overall?\r
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Algebra.Com's Answer #850331 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Let's break down this problem step-by-step:\r
\n" ); document.write( "\n" ); document.write( "**1. Calculate the Down Payment and Loan Amount**\r
\n" ); document.write( "\n" ); document.write( "* Down payment: $223,600 * 15% = $33,540
\n" ); document.write( "* Loan amount: $223,600 - $33,540 = $190,060\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the Monthly Payment for a 15-Year Loan**\r
\n" ); document.write( "\n" ); document.write( "We'll use the loan payment formula:\r
\n" ); document.write( "\n" ); document.write( "M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]\r
\n" ); document.write( "\n" ); document.write( "Where:\r
\n" ); document.write( "\n" ); document.write( "* M = Monthly payment
\n" ); document.write( "* P = Principal loan amount ($190,060)
\n" ); document.write( "* i = Monthly interest rate (annual rate / 12)
\n" ); document.write( "* n = Total number of payments (years * 12)\r
\n" ); document.write( "\n" ); document.write( "Calculations:\r
\n" ); document.write( "\n" ); document.write( "* Annual interest rate: 5.9% = 0.059
\n" ); document.write( "* Monthly interest rate (i): 0.059 / 12 ≈ 0.00491667
\n" ); document.write( "* Number of payments (n): 15 years * 12 months/year = 180 months\r
\n" ); document.write( "\n" ); document.write( "Now, plug the values into the formula:\r
\n" ); document.write( "\n" ); document.write( "M = 190060[ 0.00491667(1 + 0.00491667)^180 ] / [ (1 + 0.00491667)^180 - 1]
\n" ); document.write( "M = 190060[ 0.00491667(2.4419) ] / [ 2.4419 - 1]
\n" ); document.write( "M = 190060[ 0.012055 ] / [ 1.4419]
\n" ); document.write( "M = 190060[0.0083606]
\n" ); document.write( "M = $1588.99\r
\n" ); document.write( "\n" ); document.write( "Therefore the monthly payment will be approximately $1588.99\r
\n" ); document.write( "\n" ); document.write( "**3. Calculate the Total Amount Paid for Each Loan**\r
\n" ); document.write( "\n" ); document.write( "* 20-year loan: $1350.71/month * 240 months = $324,170.40
\n" ); document.write( "* 15-year loan: $1588.99/month * 180 months = $286,018.20\r
\n" ); document.write( "\n" ); document.write( "**4. Calculate the Total Interest Paid for Each Loan**\r
\n" ); document.write( "\n" ); document.write( "* 20-year loan interest: $324,170.40 - $190,060 = $134,110.40
\n" ); document.write( "* 15-year loan interest: $286,018.20 - $190,060 = $95,958.20\r
\n" ); document.write( "\n" ); document.write( "**5. Calculate the Overall Savings**\r
\n" ); document.write( "\n" ); document.write( "* Savings in total amount paid: $324,170.40 - $286,018.20 = $38,152.20
\n" ); document.write( "* Savings in total interest paid: $134,110.40 - $95,958.20 = $38,152.20\r
\n" ); document.write( "\n" ); document.write( "**Answers:**\r
\n" ); document.write( "\n" ); document.write( "* The monthly payment for a 15-year loan would be approximately $1588.99.
\n" ); document.write( "* The Trissels would save $38,152.20 overall by choosing the 15 year loan.
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