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?

Money Saved: $


Please Help! Thank you :)
<pre>Amount of mortgage loan: .8(198,741) = $158,992.80

Each monthly payment for 1st 10 years (to date): $1,562.37

Using the formula for the balance on the mortgage loan, we find the unpaid balance after 10 years of monthly 
payments (120 periods) to be: $147,456.55 

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

INITIAL payoff amount for 30 years: $562,453.20 (360 * 1,562.37)

INITIAL 30-year interest amount: $562,453.20 - 158,992.80 = $403,460.40 

Total amount paid over 10 years (120 months): 120(1,562.37) = $187,484.40

Initial principal/mortgage-loan: $158,992.80
Principal/mortgage-loan balance after 10 years (120 months): $147,456.55
Amount applied to initial principal/mortgage-loan in 10 years: $158,992.80 - 147,456.55 = 11,536.25
Amount applied to mortgage interest in 10 years: $187,484.40 - 11,536.25 = $175,948.15

Unpaid interest at the 10-year mark: $403,460.40 - 175,948.15 = $227,512.25

Total amount to be paid in 240 monthly periods, or in 20 years, at the NEW rate: 240(1,108.09) = $265,941.60
Interest to be paid from total paid in 240 months, or 20 years: $265,941.60 - 147,456.55 = $118,485.05

Interest saved: <font size  = 4><font color = blue><b>$227,512.25 - 118,485.05 = $109,027.20</font></font></b></pre>