Consider a home mortgage of ​$200000 at a fixed APR of 4.5​% for 25 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.

Let's calculate the values step by step.

### Given Data:
- Loan amount $ P = 200,000 $
- Annual Percentage Rate (APR) = 4.5% = 0.045
- Loan term = 25 years
- Payments are monthly, so there are $ 25 \times 12 = 300 $ months.

#### a. Calculate the monthly payment

The formula for the monthly payment $ M $ for a fixed-rate mortgage is:

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

Where:
- $ P $ is the loan amount (principal),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the number of monthly payments (loan term in months).

We can calculate each component:
- Monthly interest rate $ r = \frac{0.045}{12} $
- Number of monthly payments $ n = 300 $

Let's calculate the monthly payment.The monthly payment is approximately **$1,111.67**.

#### b. Determine the total amount paid over the term of the loan

To find the total amount paid over the loan term, we multiply the monthly payment by the total number of payments:

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

Let's calculate this.The total amount paid over the term of the loan is approximately **$333,499.49**.

#### c. Percentage of total amount paid toward the principal and interest

The amount paid toward the principal is simply the original loan amount $ P = 200,000 $. The interest paid is the difference between the total amount paid and the principal:

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

To find the percentages:
- Percentage toward the principal: $ \frac{P}{\text{Total Amount Paid}} \times 100 $
- Percentage toward interest: $ \frac{\text{Interest Paid}}{\text{Total Amount Paid}} \times 100 $

Let's calculate these percentages.Of the total amount paid:
- Approximately **59.97%** is paid toward the principal.
- Approximately **40.03%** is paid as interest.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How would the monthly payment change with a different loan term, such as 30 years?
2. What would happen if the APR was 3.5% instead of 4.5%?
3. How does the total interest paid vary with a different loan amount, like $300,000?
4. What if the payments were bi-weekly instead of monthly?
5. How do extra payments toward the principal affect the total interest paid?

**Tip:** Making additional payments directly toward the principal can significantly reduce the total interest paid over the life of the loan.

Consider a home mortgage of $200000 at a fixed APR of 4.5% for 25 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 $200,000 home mortgage at a fixed APR of 4.5% over 25 years. Understand the key financial concepts, including the amortization formula, percentage calculations, and compound interest. Suitable for college-level students studying financial mathematics.

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