document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206015>Question 1206015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want to buy a $238,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 5.5% interest for the rest. \r<BR>\n" );
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document.write( "How much money in interest will you save if you finance for 15 years instead of 30 years? </SPAN>\n" );
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document.write( "Answer:  <font color=red size=4>$129,619.80</font>\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "home value = $238,000<BR>\n" );
document.write( "down payment = 5% of home value = 0.05*238000 = $11900\r<BR>\n" );
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document.write( "loan amount = home value - down payment<BR>\n" );
document.write( "loan amount = $238,000 - $11,900<BR>\n" );
document.write( "loan amount = $226,100<BR>\n" );
document.write( "Or<BR>\n" );
document.write( "loan amount = 95% of home value (since 5% is already paid off)<BR>\n" );
document.write( "loan amount = 0.95*($238,000)<BR>\n" );
document.write( "loan amount = $226,100\r<BR>\n" );
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document.write( "Monthly payment formula<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "P = monthly payment<BR>\n" );
document.write( "L = loan amount<BR>\n" );
document.write( "i = monthly interest rate in decimal form<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "L = 226100<BR>\n" );
document.write( "i = 0.055/12\r<BR>\n" );
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document.write( "If you finance for 15 years, aka 15*12 = 180 months, then we'll have n = 180\r<BR>\n" );
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document.write( "Which leads to this monthly payment:<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "P = (226100*0.055/12)/( 1-(1+0.055/12)^(-180) )<BR>\n" );
document.write( "P = 1847.425690898<BR>\n" );
document.write( "P = 1847.43\r<BR>\n" );
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document.write( "The monthly payment for a 15 year mortgage is $1847.43<BR>\n" );
document.write( "You can use an online calculator such as this to confirm.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.calculatorsoup.com/calculators/financial/loan-calculator.php\">https://www.calculatorsoup.com/calculators/financial/loan-calculator.php</a>\r<BR>\n" );
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document.write( "If you pay $1847.43 per month for 180 months, then you'll pay back a total of $332,537.40 due to the scratch work 180*1847.43 = 332537.40<BR>\n" );
document.write( "Let A = 332537.40 since we'll refer to this value later.\r<BR>\n" );
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document.write( "Now let's consider a 30 year mortgage.<BR>\n" );
document.write( "This is over a span of 12*30 = 360 months.<BR>\n" );
document.write( "We'll have n = 360 but every other input stays the same.<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "P = (226100*0.055/12)/( 1-(1+0.055/12)^(-360) )<BR>\n" );
document.write( "P = 1283.770932046<BR>\n" );
document.write( "P = 1283.77\r<BR>\n" );
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document.write( "This time you pay back $1283.77 per month for 360 months. <BR>\n" );
document.write( "The total amount paid back is 360*1283.77 = 462157.20 dollars.<BR>\n" );
document.write( "Let's call this value B.\r<BR>\n" );
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document.write( "Subtract the two results A and B to find how much is saved.<BR>\n" );
document.write( "B - A = 462157.20 - 332537.40 = <font color=red>$129,619.80</font> which is the final answer.\r<BR>\n" );
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document.write( "Or you can compute the interest for each mortgage length and then subtract those interest values to find out how much is saved.<BR>\n" );
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