Determine the monthly principal and interest payment for a 15​-year mortgage when the amount financed is ​$85 comma 000 and the annual percentage rate​ (APR) is 7.0​%. 
.
.
.
Question content area top right
Part 1
Click here for table of Monthly PaymentsLOADING...
Question content area bottom
Part 1
The monthly principal and interest payment is ​$
  
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 of $85,000 and an annual percentage rate (APR) of 7.0%, we need to use the standard mortgage payment formula:

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

where:

- $ M $ = Monthly payment
- $ P $ = Principal amount ($85,000)
- $ r $ = Monthly interest rate (APR divided by 12 months)
- $ n $ = Total number of monthly payments (15 years × 12 months/year = 180)

### Step 1: Calculate the monthly interest rate
The annual interest rate is 7.0%, so the monthly rate is:

\[
r = \frac{7.0\%}{12} = 0.07 / 12 = 0.0058333
\]

### Step 2: Calculate the total number of payments
For a 15-year mortgage:

\[
n = 15 \times 12 = 180 \, \text{payments}
\]

### Step 3: Substitute values into the formula
\[
M = 85,000 \times \frac{0.0058333(1+0.0058333)^{180}}{(1+0.0058333)^{180} - 1}
\]

### Step 4: Compute the monthly payment
I'll calculate the value for you.The monthly principal and interest payment for a 15-year mortgage with a loan amount of $85,000 at an annual percentage rate of 7.0% is approximately **$764.00** (rounded to the nearest cent).

Would you like more details or have any questions?

### Related Questions:
1. How would the monthly payment change if the mortgage term was 30 years instead of 15?
2. What is the total interest paid over the life of this 15-year mortgage?
3. How does the monthly payment change if the interest rate decreases to 5%?
4. What portion of the first monthly payment is allocated to principal and what portion to interest?
5. How much would be saved if an additional $100 was paid monthly towards the principal?

**Tip**: The longer the loan term, the smaller the monthly payments, but the total interest paid over the life of the loan increases.

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%.

Calculate the monthly principal and interest payment for a 15-year mortgage of $85,000 at a 7.0% APR. This solution uses the standard amortization formula and breaks down key concepts like interest calculation and loan payments, suitable for advanced high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation