Determine the monthly principal and interest payment for a 20​-year mortgage when the amount financed is ​$275 comma 000 and the annual percentage rate​ (APR) is 4.5​%. 
.
.
.
Question content area top right
Part 1
Click here for table of Monthly PaymentsLOADING...
Question content area bottom
Part 1
The monthly principal and interest payment is ​$
  
enter your response here. 
​(Round to the nearest cent as​ needed.)

To determine the monthly principal and interest payment for a mortgage, we use the following mortgage payment formula:

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

Where:
- $ M $ = monthly mortgage payment (what we want to calculate),
- $ P $ = loan amount (in this case, $ P = 275,000 $),
- $ r $ = monthly interest rate (annual interest rate divided by 12),
- $ n $ = total number of payments (loan term in years multiplied by 12).

### Step 1: Convert the APR to a monthly interest rate
The annual percentage rate (APR) is 4.5%, so we divide by 12 to get the monthly rate:

\[
r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

### Step 2: Calculate the number of payments
Since this is a 20-year mortgage, the total number of payments is:

\[
n = 20 \times 12 = 240 \, \text{months}
\]

### Step 3: Plug values into the formula
Now, substitute the values into the mortgage payment formula:

\[
M = \frac{275,000 \cdot 0.00375 \cdot (1+0.00375)^{240}}{(1+0.00375)^{240} - 1}
\]

I'll calculate this to find the monthly payment.The monthly principal and interest payment for the 20-year mortgage is approximately **$1,739.79**.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:
1. How would the payment change if the APR was 5% instead of 4.5%?
2. How much total interest would you pay over the life of the loan?
3. What is the balance of the loan after 10 years of payments?
4. How does a 30-year mortgage affect the monthly payment compared to a 20-year mortgage?
5. What is the breakdown of principal and interest in the first payment?

**Tip:** A lower APR or a longer loan term reduces your monthly payment, but you end up paying more interest over time.

Determine the monthly principal and interest payment for a 20-year mortgage when the amount financed is $275,000 and the annual percentage rate (APR) is 4.5%.

Learn how to calculate the monthly mortgage payment for a 20-year loan of $275,000 with a 4.5% APR. This solution covers key finance and algebraic concepts using the mortgage payment formula. Suitable for students in Grades 10-12 and anyone learning about financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation