https://file.aiquickdraw.com/mathbot/file/1729483107778xy5qaddc.jpg

Let's solve the mortgage problem from the image.

You are given:
- Loan amount (Principal, $P$) = $225,000
- Annual Percentage Rate (APR) = 3% (or 0.03 in decimal)
- Loan term = 30 years

The formula for calculating the monthly mortgage payment is based on the **amortization formula**:

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

Where:
- $M$ is the monthly payment,
- $P$ is the principal (loan amount),
- $r$ is the monthly interest rate, which is the annual interest rate divided by 12, 
- $n$ is the total number of payments, which is the number of years times 12 (for months).

### Step 1: Find the monthly interest rate
\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

### Step 2: Find the total number of payments
\[
n = 30 \times 12 = 360
\]

### Step 3: Calculate the monthly payment
Using the amortization formula:

\[
M = 225,000 \times \frac{0.0025(1+0.0025)^{360}}{(1+0.0025)^{360} - 1}
\]

Now let me calculate this for you.The monthly mortgage payment is approximately **$948.61**.

Now, let's continue solving the other parts of the problem:

### 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:

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

Let me calculate that for you.The total amount paid over the term of the loan is approximately **$341,499.27**.

### c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?

- The **amount paid toward the principal** is the loan amount itself, which is $225,000.
- The **amount paid toward interest** is the total amount paid minus the principal.

Let me calculate these percentages for you.Of the total amount paid:
- Approximately **65.89%** is paid toward the principal.
- Approximately **34.11%** is paid toward interest.

Would you like more details or have any other questions?

Here are five related questions to explore further:
1. How does the monthly payment change if the interest rate increases to 4%?
2. How much can be saved in interest by reducing the loan term to 15 years?
3. What happens to the total interest paid if you make extra payments each month?
4. How is the amortization schedule for a mortgage structured over time?
5. How do biweekly mortgage payments impact the loan payoff time?

**Tip**: Making extra payments toward your mortgage can reduce the total interest paid and shorten the loan term.

Consider a home mortgage of $225,000 at a fixed APR of 3% 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 towards the principal and what percentage is paid for interest?

Learn how to calculate the monthly payment for a $225,000 mortgage with a 3% APR over 30 years. This detailed solution covers amortization, total interest paid, and percentage breakdown of principal and interest. Suitable for finance students and advanced high school math learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation