Consider a home mortgage of ​$250 comma 000 at a fixed APR of 3​% for 20 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.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest

We can solve the mortgage problem by using the formula for a fixed-rate mortgage's monthly payment, which is based on the loan amount, interest rate, and loan term.

### a. **Monthly Payment Calculation**

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

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

Where:
- $P = 250,000$ (the loan amount),
- $r = \frac{3\%}{12} = 0.0025$ (the monthly interest rate, annual rate divided by 12),
- $n = 20 \times 12 = 240$ (the total number of monthly payments over 20 years).

Let's calculate the monthly payment $M$.The monthly payment is approximately **$1386.49**.

### b. **Total Amount Paid Over the Term of the Loan**

To find the total amount paid over the 20 years, 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 **$332,758.56**.

### c. **Percentage Paid Toward Principal and Interest**

- The amount paid toward the principal is the original loan amount, $ P = 250,000 $.
- The amount paid toward interest is the difference between the total amount paid and the principal:

\[
\text{Interest paid} = \text{Total amount paid} - P
\]

To find the percentages:
- The percentage paid toward the principal is:

\[
\text{Percentage for principal} = \left( \frac{P}{\text{Total amount paid}} \right) \times 100
\]

- The percentage paid toward interest is:

\[
\text{Percentage for interest} = \left( \frac{\text{Interest paid}}{\text{Total amount paid}} \right) \times 100
\]

Let's calculate these values.Approximately **75.13%** of the total amount paid is toward the principal, and **24.87%** is toward interest.

Would you like further details on any of these calculations or have any other questions?

Here are 5 related questions you might find interesting:
1. How would the monthly payment change if the loan term was 30 years instead of 20?
2. What impact would an increase in the APR to 4% have on the total interest paid?
3. How does making extra payments affect the total interest paid over the life of the loan?
4. What is the remaining balance after 10 years of payments on this mortgage?
5. How is the amortization schedule calculated for this loan?

**Tip:** Increasing the frequency of payments (e.g., biweekly instead of monthly) can help you pay off the loan faster and reduce the total interest paid.

Consider a home mortgage of $250,000 at a fixed APR of 3% for 20 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 mortgage payment for a $250,000 loan with a 3% APR over 20 years. Includes step-by-step instructions on determining the total amount paid, and how to calculate the percentages toward the principal and interest.

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