Question 1109707: A person purchased a $143, 712 home 10 years ago by paying 10% down and signing a 30-year mortgage at 11.7% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 30-year mortgage at %6.6% compounded monthly. How much interest will refinancing save?
Thank you in advance
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the home is purchased for $143,712.
10% down leaves a mortgage of $129,340.8
payment on this mortgage at 11.7% per year compounded monthly is equal to 1,300.624172 per month.
if this loan went to completion, total interest would be 12 * 30 * 1,300.624172 = 458,224.7021 minus 129,340.8 = 338,883.9021
that is the total of all the payments minus the cost of the original loan.
after 10 years (120 months), the remaining balance on this loan is 120,401.032.
this is calculated by finding the present value of 240 monthly payments of 1,300.624172.
since the original loan was 360 months and it was stopped after 120 months, what remains is 240 months of payments.
the present value of those payments for 240 months gives you the remaining balance on the loan after 120 months.
the amount of the loan that has been paid off in 10 years is 129,340.8 minus 120,401.032 = 8,939.768002
the total interest paid during those 10 years is 10 * 12 * 1,300.624172 = 156,074.9007 minus 8,939.768002 = 147,135.1326.
monthly payment on the new loan at 6.6% for 30 years compounding monthly = 768.9518078.
total interest on the new loan = 12 * 30 * 768.9518078 minus 120,401.032 = 156,421.6188.
total interest on 10 years of the original loan plus total interest on the new loan = 147,135.1327 + 156,421.6188 = 303,556.7515
difference in interest on original loan if it was carried for 30 years and interest on the original loan for 10 years plus interest on the new loan = 338,8839.021 minus 303,556.7515 = 35,327.15056.
round that to two decimal places to get 35,327.15.
i used an excel spreadsheet to verify this amount is correct, given the assumptions used in solving the problem, and the excel spreadsheet confirms the solution is correct.
i also went online and used bankrate.com calculators to perform the same analysis.
bankrate.com also confirmed the solution is correct, given the assumptions used in solving the problem are correct.
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