To calculate the regular monthly payment (PMT) for a mortgage, we can use the formula you provided. Let's break down the pieces of information you have given to compute PMT step by step.
Given:
- Price of the home (P) = $350,000
- Down payment = 20% of the home's price
- Loan term (l) = 30 years
- Annual interest rate = 5.5%
- Number of payments per year (n) = 12 (monthly payments)
Steps to Calculate PMT:
-
Calculate the Down Payment and the Loan Amount:
- Down payment = 20% of $350,000 = 0.20 × $350,000 = $70,000
- Loan Amount = Price of the home - Down payment = $350,000 - $70,000 = $280,000
-
Convert the Interest Rate and Loan Term:
- Monthly interest rate (x/n) = Annual interest rate / 12 \[ = \frac{5.5%}{12} = \frac{0.055}{12} \approx 0.00458333 \]
- Total number of payments (n * l) = 12 payments/year × 30 years = 360 payments
-
Substituting Values into the PMT Formula:
- According to the provided formula, \[ PMT = \frac{P(x/n)}{1 - (1 + x/n)^{-n*l}} \] Where:
- \( P = 280,000 \) (Loan Amount)
- \( x/n \approx 0.00458333 \)
- \( n * l = 360 \)
-
Calculate PMT: \[ PMT = \frac{280,000 \times 0.00458333}{1 - (1 + 0.00458333)^{-360}} \]
First, calculate \( (1 + 0.00458333)^{-360} \): \[ (1 + 0.00458333) = 1.00458333 \]
Now, using a calculator: \[ (1.00458333)^{-360} \approx 0.173439 \]
Now calculate \( 1 - (1 + 0.00458333)^{-360} \): \[ 1 - 0.173439 \approx 0.826561 \]
Now substitute back into the PMT formula: \[ PMT \approx \frac{280,000 \times 0.00458333}{0.826561} \] Calculate the numerator: \[ 280,000 \times 0.00458333 \approx 1285.3333 \]
Finally, divide by 0.826561: \[ PMT \approx \frac{1285.3333}{0.826561} \approx 1555.11 \]
Final Monthly Payment:
Rounding to the nearest dollar, the monthly payment (PMT) is approximately: \[ \boxed{1555} \]
So, the regular monthly payment amount for this mortgage would be $1,555.
1 answer