Question

This year (10 years after you first took out the loan), you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $108,123 left to pay on your loan. Your house is now valued at $170,000.

Your current situation

How much of the original loan have you paid off? (i.e, how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)

How much money have you paid to the loan company so far (over the last 10 years)?

How much interest have you paid so far (over the last 10 years)?

How much equity do you have in your home (equity is value minus remaining debt)

Refinancing

Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate.

If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?

How much interest will you pay over the life of the new loan?

Analyzing the refinance

Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total.

How much will you save each month because of the lower monthly payment?

How much total interest will you be paying (consider the interest you paid over the first 10 years of your original loan as well as interest on your refinanced loan)

Now the non-computational question: Does it make sense to refinance? (there isn't a correct answer to this question. Just give your opinion and your reason)

Answer 1

To answer the questions, we need to perform several calculations based on the given information:

1. How much of the original loan have you paid off?

Original loan balance = $170,000 (house value) - $108,123 (remaining debt) = $61,877

2. How much money have you paid to the loan company so far (over the last 10 years)?

Total payments = Original loan - Remaining debt = $170,000 - $108,123 = $61,877

3. How much interest have you paid so far (over the last 10 years)?

Interest paid = Total payments - Original loan = $61,877 - $170,000 = -$108,123 (since the remaining debt is less than the original loan)

4. How much equity do you have in your home (equity is value minus remaining debt)?

Equity = House value - Remaining debt = $170,000 - $108,123 = $61,877

5. If you took out a new 30-year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?

Using a mortgage calculator, we can find the new monthly payments for the remaining loan balance ($108,123) with a 6% interest rate over 30 years.

6. How much interest will you pay over the life of the new loan?

Using the same mortgage calculator, we can find the total interest paid over the life of the new loan.

7. How much will you save each month because of the lower monthly payment?

Monthly savings = Current monthly payment - New monthly payment

8. How much total interest will you be paying (consider the interest you paid over the first 10 years of your original loan as well as interest on your refinanced loan)?

Total interest paid = Interest paid over the first 10 years + Total interest paid on the refinanced loan

Regarding whether it makes sense to refinance, this is a subjective question. It depends on various factors such as the amount of monthly savings, the total interest saved, how long you plan to stay in the house, and any potential costs associated with refinancing. It is essential to carefully consider all the factors and weigh the pros and cons before making a decision.