30 Year Loan Repayment Calculator

30-Year Loan Payment Formula:

\[ PMT = P \times \frac{r \times (1 + r)^{360}}{(1 + r)^{360} - 1} \]

Monthly Payment (PMT):

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1. What is the 30-Year Loan Payment Formula?

The 30-year loan payment formula calculates the fixed monthly payment required to fully repay a loan over 30 years (360 months) at a constant interest rate. This is the standard calculation for most fixed-rate mortgages in the United States.

2. How Does the Calculator Work?

The calculator uses the standard loan payment formula:

\[ PMT = P \times \frac{r \times (1 + r)^{360}}{(1 + r)^{360} - 1} \]

Where:

$ P $ — Principal loan amount (USD)
$ r $ — Monthly interest rate (annual rate ÷ 12, in decimal)
360 — Number of monthly payments (30 years × 12 months)
$ PMT $ — Monthly payment amount (USD)

Explanation: The formula accounts for compound interest over the life of the loan, calculating a fixed payment that covers both principal and interest.

3. Importance of Loan Payment Calculation

Details: Understanding your monthly payment helps with budgeting and determining how much house you can afford. Even small changes in interest rates can significantly impact your monthly payment over 30 years.

4. Using the Calculator

Tips: Enter the loan amount in USD and the annual interest rate as a percentage (e.g., 4.125). The calculator will show your estimated monthly payment for a standard 30-year fixed mortgage.

5. Frequently Asked Questions (FAQ)

Q1: Why 360 months for a 30-year loan?
A: 30 years equals 360 months (30 × 12). This is the standard term for long-term mortgages in the U.S.

Q2: Does this include taxes and insurance?
A: No, this calculates only principal and interest. Your actual mortgage payment may include escrow for property taxes and insurance.

Q3: How does interest rate affect payments?
A: Higher rates increase monthly payments significantly over 30 years. A 1% rate increase on a $300,000 loan adds about $180 to the monthly payment.

Q4: Are there prepayment penalties?
A: Most modern loans allow prepayment without penalty, but check your specific loan terms as this can save thousands in interest.

Q5: How much goes to principal vs interest?
A: Early payments are mostly interest. After 10 years on a 30-year loan, you've typically paid about 20% of the principal.