Question

Sarah Fields wants to borrow $ 132, 000 at​ 6.5% to buy a house. How much interest would she save by going with a​ 15-year mortgage over a​ 25-year mortgage?

Answer 1

Amount borrowed = $132,000
Annual interest rate = 6.50%
Monthly interest rate = 0.54167%

If period of loan is 15 years:

Period = 15 years or 180 months

Let monthly payment be $x

$x/1.0054167 + $x/1.0054167^2 + …. + $x/1.0054167^179 + $x/1.0054167^180 = $132,000
$x * (1 - (1/1.0054167)^180) / 0.0054167 = $132,000
$x * 114.79612 = $132,000
$x = $1,149.87

Monthly payment = $1,149.87

Total amount paid = 180 * Monthly payment
Total amount paid = 180 * $1,149.87
Total amount paid = $206,976.60

Total interest paid = Total amount paid - Amount borrowed
Total interest paid = $206,976.60 - $132,000
Total interest paid = $74,976.60

If period of loan is 25 years:

Period = 25 years or 300 months

Let monthly payment be $x

$x/1.0054167 + $x/1.0054167^2 + …. + $x/1.0054167^299 + $x/1.0054167^300 = $132,000
$x * (1 - (1/1.0054167)^300) / 0.0054167 = $132,000
$x * 148.10215 = $132,000
$x = $891.28

Monthly payment = $891.28

Total amount paid = 300 * Monthly payment
Total amount paid = 300 * $891.28
Total amount paid = $267,384

Total interest paid = Total amount paid - Amount borrowed
Total interest paid = $267,384 - $132,000
Total interest paid = $135,384

Total interest saved = $135,384 - $74,976.60
Total interest saved = $60,407.40