2/1 Buydown Mortgage Payment Calculator

Formula

The formula to calculate the monthly mortgage payment for a 2/1 buydown is:

\[ \text{MP} = \frac{P \cdot r1 \cdot (1 + r1)^{n1} + P \cdot r2 \cdot (1 + r2)^{n2}}{(1 + r1)^{n1} + (1 + r2)^{n2} - 1} \]

Where:

$ \text{MP} $ is the monthly mortgage payment
$ P $ is the principal loan amount
$ r1 $ is the interest rate for the first period
$ n1 $ is the number of monthly payments for the first period
$ r2 $ is the interest rate for the second period
$ n2 $ is the number of monthly payments for the second period

What is a 2/1 Buydown?

A 2/1 Buydown is a type of mortgage loan program where the borrower’s interest rate is reduced for the first two years of the loan term. This is achieved by the borrower or the home seller paying an upfront fee, or “buydown,” to the lender at the time of closing. The interest rate is reduced by 2% in the first year and 1% in the second year, hence the name 2/1 Buydown. After the initial two years, the interest rate adjusts to the agreed-upon rate for the remainder of the loan term. This type of loan can be beneficial for borrowers who expect their income to increase in the future, as it allows for lower payments in the early years of the mortgage.

Example Calculation 1

Let's assume the following values:

Principal Loan Amount ($ \text{P} $): $200,000
Interest Rate for First Period ($ \text{r1} $): 3%
Number of Monthly Payments for First Period ($ \text{n1} $): 12 months
Interest Rate for Second Period ($ \text{r2} $): 4%
Number of Monthly Payments for Second Period ($ \text{n2} $): 12 months

Step 1: Calculate the monthly payment for the first period:

\[ \text{Payment1} = \frac{200,000 \cdot 0.03 / 12 \cdot (1 + 0.03 / 12)^{12}}{(1 + 0.03 / 12)^{12} - 1} = \$1,686.42 \]

Step 2: Calculate the monthly payment for the second period:

\[ \text{Payment2} = \frac{200,000 \cdot 0.04 / 12 \cdot (1 + 0.04 / 12)^{12}}{(1 + 0.04 / 12)^{12} - 1} = \$1,706.58 \]

Step 3: Calculate the average monthly payment:

\[ \text{MP} = \frac{1,686.42 \cdot 12 + 1,706.58 \cdot 12}{12 + 12} = \$1,696.50 \]

Therefore, the monthly mortgage payment is $1,696.50.

Example Calculation 2

Let's assume the following values:

Principal Loan Amount ($ \text{P} $): $300,000
Interest Rate for First Period ($ \text{r1} $): 2.5%
Number of Monthly Payments for First Period ($ \text{n1} $): 12 months
Interest Rate for Second Period ($ \text{r2} $): 3.5%
Number of Monthly Payments for Second Period ($ \text{n2} $): 12 months

Step 1: Calculate the monthly payment for the first period:

\[ \text{Payment1} = \frac{300,000 \cdot 0.025 / 12 \cdot (1 + 0.025 / 12)^{12}}{(1 + 0.025 / 12)^{12} - 1} = \$1,187.93 \]

Step 2: Calculate the monthly payment for the second period:

\[ \text{Payment2} = \frac{300,000 \cdot 0.035 / 12 \cdot (1 + 0.035 / 12)^{12}}{(1 + 0.035 / 12)^{12} - 1} = \$1,202.85 \]

Step 3: Calculate the average monthly payment:

\[ \text{MP} = \frac{1,187.93 \cdot 12 + 1,202.85 \cdot 12}{12 + 12} = \$1,195.39 \]

Therefore, the monthly mortgage payment is $1,195.39.