Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years.  How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money. Disregard taxes.

To determine how much Larry Davis should be willing to pay to get out of a 14% mortgage and into a 10% mortgage with 25 years remaining, we will analyze the present value of both loans and compare the savings in terms of the time value of money. Here’s the step-by-step process:

### Step 1: Understanding the problem
- **Current loan (14%)**: $80,000 loan at 14% interest for 25 years.
- **New loan (10%)**: Larry wants to refinance the remaining balance into a 10% loan, also for 25 years.
- **Objective**: Find how much Larry is willing to pay to exit the 14% loan and enter the 10% loan.

### Step 2: Calculate Monthly Payments for the 14% Mortgage
Using the mortgage payment formula:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $ M $ = monthly payment
- $ P $ = principal ($80,000)
- $ r $ = monthly interest rate (14% annual rate / 12 months = 0.014 / 12)
- $ n $ = number of payments (25 years × 12 months = 300 months)

Now let's compute the monthly payment for the 14% mortgage.

### Step 3: Calculate Monthly Payments for the 10% Mortgage
We will use the same formula as above, but this time with a 10% annual interest rate over 25 years. The new interest rate $ r $ will be 10%/12.

### Step 4: Calculate the Present Value of the 14% Mortgage
The present value of the remaining payments at the new interest rate (10%) will help us determine how much the current mortgage is worth in today's terms.

Finally, I’ll calculate both these values to determine how much Larry will save and how much he should be willing to pay to refinance his mortgage.

Let me compute these values.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you through the steps to calculate the values manually. Let me know how you'd like to proceed or if you have further questions!

In the meantime, here are some related questions that can help deepen understanding:

1. How does changing the interest rate affect the total mortgage cost over time?
2. What is the impact of a higher loan term on monthly mortgage payments?
3. Why is the time value of money important when comparing mortgage options?
4. What other factors might influence a decision to refinance a mortgage, aside from interest rates?
5. How can prepayment penalties affect the decision to refinance a mortgage?

**Tip**: Understanding the time value of money is key to making informed financial decisions, especially when comparing different mortgage options.

Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years. How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money. Disregard taxes.

Explore how to calculate the cost of refinancing a mortgage from 14% interest to 10% with 25 years remaining. This problem involves calculating the present value of annuities, the time value of money, and comparing loan amortization schedules. Suitable for advanced high school or college students.

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