You have been living in the house you bought 10 years ago for $300,000. At that time, you took out a loan for 80% of the house at a fixed rate 15-year loan at an annual stated rate of 9%. You have just paid off the 120th monthly payment. Interest rates have meanwhile dropped steadily to 6% per year, and you think it is finally time to refinance the remaining balance. But there is a catch. The fee to refinance your loan is $4,000. Should you refinance the remaining balance? How much would you save/lose if you decided to refinance?

interest rates dropping at 6% a year for 10 years?

To determine whether you should refinance the remaining balance and how much you would save or lose, we need to compare the costs and benefits involved.

First, let's calculate the remaining balance on your loan. Since you have made 120 monthly payments on a 15-year loan, the number of months remaining would be 180 - 120 = 60 months.

Next, we need to calculate the remaining loan amount. The original loan amount was 80% of the house price, which is 0.8 * $300,000 = $240,000. Since you've made 120 monthly payments, we can calculate the principal amount you've already paid off.

Using an amortization calculator or loan table, you can find that after 120 monthly payments of equal amounts, about $110,259.70 of principal would be paid off. Therefore, the remaining balance would be $240,000 - $110,259.70 = $129,740.30.

Now let's compare the costs and benefits of refinancing. The refinance fee is $4,000, so you would have to pay this upfront.

To calculate the new monthly payment at the lower interest rate, we can use a mortgage calculator or formula. With a remaining balance of $129,740.30 and an annual interest rate of 6%, the new monthly payment would be approximately $1,099.99.

If you continue paying the remaining balance on the current loan, your monthly payment at the fixed rate of 9% would be approximately $2,506.11. Subtracting the new monthly payment under the refinanced loan, we can determine the monthly savings: $2,506.11 - $1,099.99 = $1,406.12.

Now let's calculate the total savings over the remaining 5 years (60 months). With the current loan, your remaining payments would amount to $2,506.11 * 60 = $150,366.60.

If you refinance, your remaining payments would amount to $1,099.99 * 60 = $65,999.40.

Comparing the total payments under both scenarios, you can calculate the savings: $150,366.60 - $65,999.40 = $84,367.20.

However, remember that you would have to deduct the $4,000 in refinancing fees. So the net savings would be $84,367.20 - $4,000 = $80,367.20.

Therefore, if you decide to refinance the remaining balance, you would save approximately $80,367.20 over the remaining term of the loan.