Consider a home mortgage of ​$225 comma 000 at a fixed APR of 4.5​% for 15 years.
a. Calculate the monthly payment. ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
b. Determine the total amount paid over the term of the loan. ​(Round to the nearest cent as​ needed.)
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest. ​(Round to one decimal place as​ needed.)

To solve this problem, we'll use the standard formula for calculating monthly mortgage payments for a fixed-rate mortgage:

### Formula for monthly payment:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (in this case, $225,000).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12).

### Given:
- Principal $ P = 225,000 $
- Annual interest rate $ APR = 4.5\% = 0.045 $
- Loan term = 15 years

#### Part A: Calculate the monthly payment

Step 1: Convert the annual interest rate to a monthly interest rate:

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

Step 2: Determine the total number of monthly payments over 15 years:

\[
n = 15 \times 12 = 180
\]

Now, plug these values into the formula to calculate the monthly payment $ M $.

Let me calculate this for you.The monthly mortgage payment is approximately **$1,721.23**.

#### Part B: Determine the total amount paid over the term of the loan

To calculate the total amount paid, we multiply the monthly payment by the total number of payments:

\[
\text{Total Amount Paid} = M \times n
\]

Let's calculate that now.The total amount paid over the term of the loan is approximately **$309,822.28**.

#### Part C: Calculate the percentage paid toward the principal and the interest

1. **Principal**: The amount borrowed is $ P = 225,000 $.
2. **Interest**: The total interest paid is the difference between the total amount paid and the principal:

\[
\text{Interest Paid} = \text{Total Amount Paid} - P
\]

Let's calculate these percentages.- The total interest paid over the loan term is approximately **$84,822.28**.
- **72.6%** of the total payments go toward the principal.
- **27.4%** of the total payments go toward interest.

Would you like further clarification on any part of the solution?

Here are 5 related questions you may find helpful:
1. How would the monthly payment change with a different interest rate?
2. What would be the total interest paid if the loan term were extended to 30 years?
3. How does the loan principal affect the monthly payment?
4. What happens if extra payments are made toward the principal each month?
5. How can mortgage refinancing reduce interest payments?

**Tip:** The longer the loan term, the more interest you'll pay over time, even if the monthly payments are lower.

Consider a home mortgage of $225,000 at a fixed APR of 4.5% for 15 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 for a $225,000 home mortgage at a 4.5% fixed APR over 15 years. This example walks through the detailed steps to determine monthly payments, the total amount paid, and the breakdown between principal and interest payments.

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