To calculate the monthly payment for a townhome priced at $122,250 with a 10% down payment and financed with a 20-year fixed-rate mortgage at an interest rate of 5.75%, follow these steps:
-
Calculate the Down Payment: \[ \text{Down Payment} = \text{Price} \times \text{Down Payment Percentage} \] \[ \text{Down Payment} = 122,250 \times 0.10 = 12,225 \]
-
Calculate the Loan Amount: \[ \text{Loan Amount} = \text{Price} - \text{Down Payment} \] \[ \text{Loan Amount} = 122,250 - 12,225 = 110,025 \]
-
Use the Mortgage Payment Formula: The formula for calculating the monthly mortgage payment \( M \) is given by: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where:
- \( P \) = Loan amount ($110,025)
- \( r \) = Monthly interest rate = Annual interest rate / 12
- \( n \) = Total number of payments (loan term in months = years × 12)
First, calculate the monthly interest rate: \[ r = \frac{5.75%}{100} / 12 = \frac{0.0575}{12} = 0.00479167 \]
Now, calculate \( n \): \[ n = 20 \times 12 = 240 \]
-
Calculate the Monthly Payment: Plugging in the values: \[ M = 110,025 \times \frac{0.00479167(1 + 0.00479167)^{240}}{(1 + 0.00479167)^{240} - 1} \]
Calculate \( (1 + r)^n \): \[ (1 + 0.00479167)^{240} \approx 3.103676 \]
Now substitute this back into the formula: \[ M = 110,025 \times \frac{0.00479167 \times 3.103676}{3.103676 - 1} \] \[ M = 110,025 \times \frac{0.014864}{2.103676} \] \[ M = 110,025 \times 0.00706678 \approx 777.4 \]
This computation appears to be slightly off from your stated monthly payment of $772; slight variations can occur based on rounding and different methods of computation.
However, if you have calculated $772, it may be derived with adjusted specifics in financial calculators or mortgage tables. The basic formula presented demonstrates the methodology to get close results.
1 answer