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

 

Cost	 
$
400,000
 
Length of loan	 
30
  years
Interest rate	 
1.00
%
  annually
Number of payments per year	 
12
 
Down payment	 
20
%

To find the monthly mortgage payment, we can use the following mortgage payment formula, which accounts for the loan amount, interest rate, and number of payments:

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

Where:
- $M$ is the monthly mortgage payment.
- $P$ is the principal loan amount (i.e., the total loan after subtracting the down payment).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of payments (loan term in years multiplied by 12).

### Step 1: Calculate the principal
The down payment is 20% of the total cost. So, the loan amount (principal $P$) is:

\[
P = \text{Cost} \times (1 - \text{Down Payment Percentage})
\]

\[
P = 400,000 \times (1 - 0.20) = 400,000 \times 0.80 = 320,000
\]

### Step 2: Calculate the monthly interest rate
The annual interest rate is 1%, so the monthly interest rate is:

\[
r = \frac{1\%}{12} = \frac{0.01}{12} = 0.0008333
\]

### Step 3: Calculate the total number of payments
The loan length is 30 years, with 12 payments per year, so the total number of payments is:

\[
n = 30 \times 12 = 360
\]

### Step 4: Calculate the monthly payment
Now, we can substitute the values into the mortgage formula:

\[
M = 320,000 \times \frac{0.0008333(1+0.0008333)^{360}}{(1+0.0008333)^{360} - 1}
\]

I'll compute the result.The monthly mortgage payment is **$1,029.25**, rounded to the nearest cent.

Would you like more details or have any questions about the process?

Here are 5 related questions to deepen your understanding:
1. How does a higher interest rate affect monthly mortgage payments?
2. What impact does a shorter loan term (e.g., 15 years) have on monthly payments?
3. How does increasing the down payment affect the total amount of interest paid over the loan term?
4. What happens to the mortgage if payments are made bi-weekly instead of monthly?
5. How can refinancing a mortgage help lower the monthly payment?

**Tip**: Making extra payments toward your principal can significantly reduce the total interest you pay 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: $400,000; Length of loan: 30 years; Interest rate: 1.00% annually; Number of payments per year: 12; Down payment: 20%

Learn how to calculate the monthly mortgage payment for a $400,000 loan with a 1% annual interest rate, a 30-year term, and a 20% down payment. Using the mortgage payment formula, this detailed guide walks through each step to arrive at a monthly payment of $1,029.25.

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