https://file.aiquickdraw.com/mathbot/file/1727499280363bm2p7wm2.jpg

To help solve the problem in the image, I will break down the given information and apply the relevant financial formulas.

### Given:
- **Loan amount**: $261,000
- Two offers:
  - **Credit Union (Offer A)**: 15-year loan, 5.1% annual interest rate.
  - **Bank (Offer B)**: 40-year loan, 1.9% annual interest rate.

To solve the monthly mortgage payments, we use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal ($261,000)
- $ r $ = monthly interest rate (annual interest rate divided by 12)
- $ n $ = total number of monthly payments (loan term in years multiplied by 12)

### (a) **Credit Union Offer:**
- **15-year loan** at **5.1%** annual interest rate.
  - Monthly interest rate $ r = \frac{5.1}{100 \times 12} = \frac{5.1}{1200} = 0.00425 $
  - Total number of payments $ n = 15 \times 12 = 180 $

### (b) **Bank Offer:**
- **40-year loan** at **1.9%** annual interest rate.
  - Monthly interest rate $ r = \frac{1.9}{100 \times 12} = \frac{1.9}{1200} = 0.00158333 $
  - Total number of payments $ n = 40 \times 12 = 480 $

### (c) **Comparison of Total Payments:**
We will calculate the total amount paid for both loans by multiplying the monthly payment by the number of months and then compare them to determine the better deal.

Let me calculate these values now.Here are the results:

### (a) **Credit Union Offer (15-year loan at 5.1%)**:
- **Monthly payment**: \$2,077.59
- **Total payment over 15 years**: \$373,966.73

### (b) **Bank Offer (40-year loan at 1.9%)**:
- **Monthly payment**: \$776.71
- **Total payment over 40 years**: \$372,820.42

### (c) **Comparison**:
- The **total payment** with the **Credit Union** would be \$1,146.31 **more** than with the Bank.
- Therefore, the **Bank** offers the lower total payment by \$1,146.31.

Would you like a breakdown of these calculations or more details?

Here are 5 related questions for further understanding:
1. How does the length of the loan term impact the total amount paid in interest?
2. What would the monthly payment be if the interest rate for the bank increased to 2.5%?
3. How much more interest is paid with the 40-year loan compared to the 15-year loan?
4. If Ashley plans to pay off the loan early, how would that affect her total payments?
5. How would the results change if Ashley made additional payments toward the principal?

**Tip**: Longer loan terms usually result in lower monthly payments, but significantly more paid in interest over time.

Ashley is taking out a mortgage for $261,000 to buy a new house and is deciding between two offers from lenders. One lender offers a 15-year loan at a 5.1% interest rate, and the other offers a 40-year loan at a 1.9% interest rate. Calculate the monthly payments for both and determine which option results in a lower total payment over the life of the loan.

Learn how to compare two mortgage offers for a $261,000 loan. This problem involves calculating monthly payments for a 15-year loan at 5.1% interest and a 40-year loan at 1.9% interest. Understand how loan term length and interest rate impact total payments.

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