Simple/Fixed Rate Mortgage (FRM) Payment Calculator

What is a Fixed Rate Mortgage?

A Fixed Rate Mortgage (FRM) is a type of home loan where the interest rate remains the same for the entire term of the loan. This means that the monthly mortgage payment will not change over time, providing stability and predictability for the borrower.

Formula for Calculating Monthly Mortgage Payment

The formula to calculate the monthly mortgage payment is:

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

Where:

• \(M\) = Monthly Payment
• \(P\) = Loan Amount (Principal)
• \(r\) = Monthly Interest Rate
• \(n\) = Number of Payments

Step-by-Step Calculation

1. Determine the loan amount (\(P\)): \[P = \$\text{0}\]
2. Calculate the monthly interest rate (\(r\)): \[r = \frac{\text{0}}{1200} = \text{0}\]
3. Calculate the number of payments (\(n\)): \[n = \text{0} \times 12 = \text{0}\]
4. Calculate the monthly payment (\(M\)) using the formula: \[M = \text{0} \times \frac{\text{0}(1+\text{0})^{\text{0}}}{(1+\text{0})^{\text{0}}-1} = \$\text{0}\]
5. Calculate the total payment: \[ \text{Total Payment} = \text{0} \times \text{0} = \$\text{0}\]
6. Calculate the total interest paid: \[ \text{Total Interest} = \text{0} - \text{0} = \$\text{0}\]

Example Calculation

Let's calculate the monthly mortgage payment for a loan with the following details:

• Loan Amount (\(P\)): $200,000
• Annual Interest Rate: 5%
• Term: 30 years

Using the formula, we get:

1. Loan amount: \(P = \$200,000\)
2. Monthly interest rate: \[r = \frac{5}{1200} = 0.004167\]
3. Number of payments: \[n = 30 \times 12 = 360\]
4. Monthly payment: \[M = 200,000 \times \frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360}-1} = \$1,073.64\]
5. Total payment: \[ \text{Total Payment} = 1,073.64 \times 360 = \$386,510.40\]
6. Total interest paid: \[ \text{Total Interest} = 386,510.40 - 200,000 = \$186,510.40\]

Visual Representation

The green portion of the bar represents the total payment ($386,510.40) relative to the loan amount ($200,000).