Consider a home mortgage of ​$125,000 at a fixed APR of 4.5​% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
Question content area bottom
Part 1
a. The monthly payment is ​$enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
Part 2
b. The total amount paid over the term of the loan is ​$enter your response here.
​(Round to the nearest cent as​ needed.)
Part 3
c. Of the total amount​ paid, enter your response here​% is paid toward the​ principal, and enter your response here​% is paid for interest.
​(Round to one decimal place as​ needed.)

This problem involves calculating monthly mortgage payments using the loan amount, interest rate, and the loan term. We can use the following mortgage payment formula to compute the monthly payment (denoted as $ M $):

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

Where:
- $ P $ is the loan amount (\$125,000),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (loan term in years multiplied by 12).

### Part 1: Calculate the Monthly Payment
Given:
- Loan amount $ P = 125,000 $
- Annual interest rate = 4.5% or 0.045
- Loan term = 30 years

#### Step 1: Convert the annual interest rate to the monthly interest rate:
\[
r = \frac{0.045}{12} = 0.00375
\]

#### Step 2: Calculate the number of monthly payments:
\[
n = 30 \times 12 = 360
\]

#### Step 3: Plug values into the formula:
\[
M = 125,000 \times \frac{0.00375(1 + 0.00375)^{360}}{(1 + 0.00375)^{360} - 1}
\]

Let's calculate this to find the monthly payment.

I'll do the computation now.The monthly payment is approximately **\$633.36**.

### Part 2: Determine the Total Amount Paid Over the Term of the Loan

To find the total amount paid, multiply the monthly payment by the total number of payments:
\[
\text{Total Amount Paid} = M \times n
\]
I'll compute this next.The total amount paid over the term of the loan is approximately **\$228,008.39**.

### Part 3: Calculate the Percentage Paid Toward Principal and Interest

1. **Principal**: The principal amount is the original loan amount, \$125,000.
2. **Interest**: The total interest paid is the difference between the total amount paid and the principal:
   \[
   \text{Interest Paid} = \text{Total Amount Paid} - \text{Principal}
   \]
3. **Percentage toward Principal**:
   \[
   \text{Percentage toward Principal} = \left(\frac{\text{Principal}}{\text{Total Amount Paid}}\right) \times 100
   \]
4. **Percentage toward Interest**:
   \[
   \text{Percentage toward Interest} = 100 - \text{Percentage toward Principal}
   \]

I'll compute these values now.1. The total interest paid over the term of the loan is approximately **\$103,008.39**.
2. **54.8%** of the total amount paid goes toward the principal.
3. **45.2%** of the total amount paid goes toward interest.

Would you like more details or clarifications? Here are five follow-up questions related to this problem:

1. How would the monthly payment change if the interest rate was increased to 5%?
2. What is the effect of shortening the loan term to 15 years?
3. How much interest would be saved if you paid an additional \$100 per month toward the principal?
4. How does changing the loan amount to \$150,000 affect the total interest paid?
5. How does the monthly payment compare if you use a variable interest rate?

**Tip:** A lower interest rate or a shorter loan term can significantly reduce the total interest paid over the life of a loan.

Consider a home mortgage of ​$125,000 at a fixed APR of 4.5​% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

Learn how to calculate the monthly payment, total amount paid, and the percentage of principal and interest for a $125,000 mortgage at a 4.5% APR over 30 years. Includes step-by-step formulas for calculating monthly payments and percentage breakdowns.

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