Consider a home mortgage of ​$125,000 at a fixed APR of 12​% 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.

Given the home mortgage scenario with a principal of $125,000, a fixed APR of 12%, and a term of 15 years, we will calculate the monthly payment, the total amount paid, and the breakdown of the payments toward principal and interest. Here's how we can proceed step by step:

### Part (a): Calculate the Monthly Payment
To calculate the monthly mortgage payment, we use the standard amortization formula:

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

Where:
- $M$ is the monthly payment.
- $P$ is the loan amount (principal), which is $125,000.
- $r$ is the monthly interest rate, calculated as $r = \frac{APR}{12}$.
- $n$ is the total number of payments, calculated as $n = \text{years} \times 12$.

Let’s plug in the values:
- $P = 125,000$
- Annual interest rate (APR) = 12%, so the monthly interest rate $r = \frac{12\%}{12} = 0.01$ (or 1%).
- The number of payments for a 15-year loan is $n = 15 \times 12 = 180$.

Now, let's calculate the monthly payment.

### Part (b): Determine the Total Amount Paid Over the Term of the Loan
The total amount paid is simply the monthly payment multiplied by the total number of payments:
\[
\text{Total amount paid} = M \times n
\]

### Part (c): Calculate the Percentage Paid Toward Principal and Interest
- The total interest paid is the difference between the total amount paid and the loan principal.
\[
\text{Total interest} = \text{Total amount paid} - P
\]
- The percentage of the total amount paid toward the principal is:
\[
\text{Percentage paid toward principal} = \left(\frac{P}{\text{Total amount paid}}\right) \times 100
\]
- The percentage of the total amount paid toward interest is:
\[
\text{Percentage paid toward interest} = \left(\frac{\text{Total interest}}{\text{Total amount paid}}\right) \times 100
\]

Let's compute these values.### Results:
(a) The **monthly payment** is approximately **$1,500.21**.

(b) The **total amount paid** over the term of the loan is approximately **$270,037.81**.

(c) Of the total amount paid:
- **46.29%** is paid toward the principal.
- **53.71%** is paid toward interest.

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How would the monthly payment change if the loan term was 30 years instead of 15 years?
2. What is the impact of increasing the interest rate on total interest paid?
3. How does making extra payments on a mortgage affect the loan term and interest?
4. How would a down payment affect the monthly mortgage payment and total interest?
5. What are the benefits of refinancing a mortgage with a lower APR?

**Tip:** Paying extra toward your mortgage principal reduces the interest you pay over time, potentially saving thousands of dollars.

Consider a home mortgage of ​$125,000 at a fixed APR of 12​% 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, total amount paid, and interest breakdown for a $125,000 mortgage at 12% APR over 15 years. Understand loan amortization and the percentages of payments toward principal and interest.

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