document.write( "Question 1189735: A person purchased a ​$198741 home 10 years ago by paying ​20% down and signing a​ 30-year mortgage at 11.4​% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20​-year mortgage at compounded 6.6% monthly. How much interest will refinancing​ save?\r
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Algebra.Com's Answer #821482 by MathTherapy(10552)\"\" \"About 
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\n" ); document.write( "A person purchased a ​$198741 home 10 years ago by paying ​20% down and signing a​ 30-year mortgage at 11.4​% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20​-year mortgage at compounded 6.6% monthly. How much interest will refinancing​ save?\r
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Amount of mortgage loan: .8(198,741) = $158,992.80\r\n" );
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document.write( "Each monthly payment for 1st 10 years (to date): $1,562.37\r\n" );
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document.write( "Using the formula for the balance on the mortgage loan, we find the unpaid balance after 10 years of monthly \r\n" );
document.write( "payments (120 periods) to be: $147,456.55 \r\n" );
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document.write( "Over the next 20 years, and at a 6.6% annual interest rate, each monthly payment to pay off balance ($147,456.55), is $1,108.09\r\n" );
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document.write( "INITIAL payoff amount for 30 years: $562,453.20 (360 * 1,562.37)\r\n" );
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document.write( "INITIAL 30-year interest amount: $562,453.20 - 158,992.80 = $403,460.40 \r\n" );
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document.write( "Total amount paid over 10 years (120 months): 120(1,562.37) = $187,484.40\r\n" );
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document.write( "Initial principal/mortgage-loan: $158,992.80\r\n" );
document.write( "Principal/mortgage-loan balance after 10 years (120 months): $147,456.55\r\n" );
document.write( "Amount applied to initial principal/mortgage-loan in 10 years: $158,992.80 - 147,456.55 = 11,536.25\r\n" );
document.write( "Amount applied to mortgage interest in 10 years: $187,484.40 - 11,536.25 = $175,948.15\r\n" );
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document.write( "Unpaid interest at the 10-year mark: $403,460.40 - 175,948.15 = $227,512.25\r\n" );
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document.write( "Total amount to be paid in 240 monthly periods, or in 20 years, at the NEW rate: 240(1,108.09) = $265,941.60\r\n" );
document.write( "Interest to be paid from total paid in 240 months, or 20 years: $265,941.60 - 147,456.55 = $118,485.05\r\n" );
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document.write( "Interest saved: $227,512.25 - 118,485.05 = $109,027.20
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