Consider a home mortgage of ​$200 comma 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.
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Part 1
a. The monthly payment is ​

To calculate the monthly payment for a fixed-rate mortgage, we use the formula for the monthly mortgage payment $ M $:

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

Where:
- $ P $ = Loan principal (initial 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 = 200,000 $
- Annual interest rate = 4.5% or 0.045
- Loan term = 15 years

Now let's break it down:

- Monthly interest rate $ r = \frac{0.045}{12} $
- Total number of payments $ n = 15 \times 12 $

Let me calculate the monthly payment using these values.The monthly payment for the mortgage is approximately **$1,529.99**.

### Part (b): Determining 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. Let me calculate that for you.The total amount paid over the term of the loan is approximately **$275,397.58**.

### Part (c): Percentage paid toward principal and interest

To find the percentage of the total amount paid toward the principal and interest:
- The total principal paid is the original loan amount ($P = 200,000$).
- The total interest paid is the difference between the total amount paid and the principal.

Now, I will calculate the percentages.Of the total amount paid:
- **72.62%** is paid toward the principal.
- **27.38%** is paid toward interest.

Would you like further details on any of these calculations?

### Here are 5 related questions you might find interesting:
1. How would the monthly payment change if the loan term were extended to 30 years?
2. What would be the impact of a higher interest rate on the monthly payment?
3. How can making additional payments affect the total interest paid?
4. How does an adjustable-rate mortgage differ in terms of payment structure compared to a fixed-rate mortgage?
5. What are the tax implications of mortgage interest deductions?

#### Tip:
Paying even a small extra amount toward your principal each month can significantly reduce the total interest you pay over the life of the loan!

Consider a home mortgage of $200,000 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 $200,000 mortgage at 4.5% APR for 15 years. Find out the total amount paid over the loan term and determine the percentage of payments toward the principal and interest. This detailed solution covers key financial concepts like amortization and interest calculation.

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