Consider a home mortgage of 

​$150 comma 000150,000 

at a fixed APR of 

66​% 

for 

3030 

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.)

To solve this problem, we'll use the formula for calculating the monthly payment on a fixed-rate mortgage. The formula for the monthly mortgage payment is:

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

Where:
- $ M $ = monthly payment
- $ P $ = principal loan amount
- $ r $ = monthly interest rate (annual interest rate divided by 12)
- $ n $ = total number of payments (loan term in years multiplied by 12)

### Given:
- $ P = 150,000 $ (principal)
- Annual Percentage Rate (APR) = 6% = 0.06
- Loan term = 30 years = 360 months

#### Step 1: Calculate the monthly interest rate
\[
r = \frac{0.06}{12} = 0.005
\]

#### Step 2: Calculate the total number of payments
\[
n = 30 \times 12 = 360 \text{ payments}
\]

#### Step 3: Substitute values into the formula

Now, I'll calculate the monthly payment $ M $ using these values.The monthly mortgage payment is approximately **$899.33**.

### Part b: Total Amount Paid
To find the total amount paid over the term of the loan, we multiply the monthly payment by the total number of payments:

\[
\text{Total amount paid} = M \times n
\]

Let me calculate that next.The total amount paid over the term of the loan is approximately **$323,757.28**.

### Part c: Percentage of Total Paid Toward Principal and Interest

To determine how much is paid toward the principal and interest:
- The amount paid toward the principal is the loan amount: $150,000.
- The interest paid is the total amount paid minus the principal.

Let's calculate the interest paid and the percentage paid toward principal and interest.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the interest and percentages manually using the following steps:

1. **Interest Paid**:
   \[
   \text{Interest Paid} = \text{Total Amount Paid} - \text{Principal}
   = 323,757.28 - 150,000 = 173,757.28
   \]

2. **Percentage Paid Toward Principal**:
   \[
   \text{Percentage of Principal} = \left(\frac{150,000}{323,757.28}\right) \times 100 = 46.33\%
   \]

3. **Percentage Paid Toward Interest**:
   \[
   \text{Percentage of Interest} = \left(\frac{173,757.28}{323,757.28}\right) \times 100 = 53.67\%
   \]

So, about **46.33%** is paid toward the principal, and **53.67%** is paid for interest.

Let me know if you'd like more details or clarification!

Here are some related questions:
1. How do different APR values affect the monthly payment?
2. What would be the impact of a shorter loan term, such as 15 years, on the payment and interest?
3. How does compounding affect interest calculation in mortgages?
4. How would an extra payment each year affect the loan term?
5. What is the difference between APR and the nominal interest rate?

**Tip:** Paying extra toward the principal each month can significantly reduce the interest paid over the life of the loan.

Consider a home mortgage of $150,000 at a fixed APR of 6% 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 on a $150,000 mortgage at a 6% APR for 30 years. Understand loan amortization, calculate total interest paid, and determine the percentage paid toward the principal and interest.

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