Question

What is the monthly payment for this mortgage, as shown in the table below?  Round to the nearest cent.
 
Cost

$200,000

Length of loan

30 years

Interest rate

3.00% annually

Number of payment per year

12

Down payment

$10,000

To calculate the monthly mortgage payment, we will use the **standard formula for a fixed-rate mortgage**, which is:

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

Where:
- $ M $ = Monthly payment
- $ P $ = Loan principal (the amount of the loan after the down payment)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments (number of years multiplied by the number of payments per year)

Let's break it down:

### Step 1: Determine the loan principal.
The total cost of the house is $200,000, and the down payment is $10,000. So, the loan principal $ P $ is:
\[
P = 200,000 - 10,000 = 190,000
\]

### Step 2: Calculate the monthly interest rate.
The annual interest rate is 3%, so the monthly interest rate $ r $ is:
\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

### Step 3: Calculate the total number of payments.
The loan term is 30 years, with 12 payments per year, so the total number of payments $ n $ is:
\[
n = 30 \times 12 = 360
\]

### Step 4: Plug these values into the formula.
\[
M = 190,000 \cdot \frac{0.0025(1+0.0025)^{360}}{(1+0.0025)^{360} - 1}
\]

I'll calculate this now.The monthly mortgage payment is approximately **$801.05**, rounded to the nearest cent.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions:
1. How would the monthly payment change with a higher interest rate, like 4%?
2. What if the loan term was 15 years instead of 30 years?
3. How does the size of the down payment affect the monthly mortgage payment?
4. What is the total interest paid over the life of the loan in this scenario?
5. How can making extra payments affect the overall cost of the loan?

**Tip:** Paying a little extra each month towards the principal can significantly reduce the total interest paid over the life of the loan.

What is the monthly payment for this mortgage, as shown in the table below? Round to the nearest cent. Cost: $200,000, Length of loan: 30 years, Interest rate: 3.00% annually, Number of payments per year: 12, Down payment: $10,000.

Learn how to calculate the monthly mortgage payment for a $200,000 home loan with a 3% annual interest rate over 30 years. This step-by-step guide covers important concepts such as interest rates, loan amortization, and the standard mortgage formula, suitable for high school or college finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation