Determine the monthly principal and interest payment for a 15​-year mortgage when the amount financed is ​$85 comma 000 and the annual percentage rate​ (APR) is 7.0​%. 
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The monthly principal and interest payment is ​$
  
enter your response here. 
​(Round to the nearest cent as​ needed.)

To determine the monthly principal and interest payment for a 15-year mortgage with an amount financed of $85,000 and an APR of 7.0%, we can use the following formula for monthly mortgage payments:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the loan principal (the amount financed), which is $85,000.
- $ r $ is the monthly interest rate (the annual rate divided by 12). So, $ r = \frac{7\%}{12} = 0.07/12 = 0.0058333 $.
- $ n $ is the total number of payments (the loan term in months). For a 15-year mortgage, $ n = 15 \times 12 = 180 $ months.

Let's calculate this step by step.

### Step 1: Identify the values.
- $ P = 85,000 $
- $ r = 0.0058333 $
- $ n = 180 $

### Step 2: Plug the values into the formula and calculate.

\[
M = 85,000 \times \frac{0.0058333(1 + 0.0058333)^{180}}{(1 + 0.0058333)^{180} - 1}
\]

Now, I will calculate this.

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However, if you would like, I can walk you through the steps for calculating this manually or using a calculator. Let me know how you'd like to proceed!

Do you have any questions or want more details?

Here are 5 related questions:
1. How is the mortgage payment formula derived?
2. How would a 30-year mortgage affect the monthly payments?
3. What happens if the APR changes during the mortgage term?
4. How do you calculate the total interest paid over the life of the loan?
5. How does a down payment affect the loan principal?

**Tip**: The lower the interest rate or the shorter the loan term, the less you pay in total interest over the life of the loan.

Determine the monthly principal and interest payment for a 15​-year mortgage when the amount financed is ​$85,000 and the annual percentage rate​ (APR) is 7.0​%. Round to the nearest cent as needed.

This page provides a detailed solution for calculating the monthly mortgage payment for a 15-year loan of $85,000 at a 7% APR. It explains the formula used to find the payment, including finance math concepts like the annuity formula and exponential growth.

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