A person purchased a 141797$ home 10 years ago by paying 20% down and signing a 30-year mortgage at 10.5 % compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at compounded 6.9%monthly. How much interest will refinancing save?
To determine how much interest the owner will save by refinancing, we need to calculate the interest paid under both the current and the new mortgage terms.
First, let's calculate the current mortgage details:
Loan amount (initial home price - down payment): $141,797 - (20% x $141,797) = $141,797 - $28,359.40 = $113,437.60
Number of monthly payments: 30 years x 12 months = 360 months
Monthly interest rate: 10.5% / 12 = 0.875%
Next, we can calculate the monthly payment under the current mortgage using the formula for a fixed-rate mortgage:
P = principal loan amount = $113,437.60
r = monthly interest rate = 0.875%
n = total number of monthly payments = 360
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
With the given values, the monthly payment under the current mortgage is approximately $960.44.
Now, let's calculate the new mortgage details:
Number of monthly payments: 20 years x 12 months = 240 months
Monthly interest rate: 6.9% / 12 = 0.575%
Using the same formula as above, we can calculate the new monthly payment:
P = principal loan amount = $113,437.60
r = monthly interest rate = 0.575%
n = total number of monthly payments = 240
New monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
With the given values, the new monthly payment is approximately $928.32.
To find the interest paid under each mortgage, we can multiply the monthly payment by the total number of payments and subtract the initial loan amount:
Interest paid under the current mortgage = (monthly payment) * (number of payments) - initial loan amount
= ($960.44) * (360) - $113,437.60
= $345,757.40 - $113,437.60
= $232,319.80
Interest paid under the new mortgage = (monthly payment) * (number of payments) - initial loan amount
= ($928.32) * (240) - $113,437.60
= $222,796.80 - $113,437.60
= $109,359.20
Finally, we can calculate the interest saved by refinancing:
Interest saved = Interest paid under the current mortgage - Interest paid under the new mortgage
= $232,319.80 - $109,359.20
= $122,960.60
Therefore, refinancing will save approximately $122,960.60 in interest.