Welcome to the Bankrate Mortgage Payment Calculator. Use this tool to quickly estimate your monthly mortgage payments based on the principal loan amount, interest rate, and term length. Accurate financial planning starts here.
Mortgage Payment Calculator
Mortgage Payment Formula
The standard formula used to calculate the fixed monthly payment (M) for a loan is:
$$ M = P \left[ \frac{i(1+i)^n}{(1+i)^n – 1} \right] $$Where:
- $P$ = Principal Loan Amount
- $i$ = Monthly Interest Rate (Annual Rate / 1200)
- $n$ = Total Number of Payments (Loan Term in Years × 12)
Formula Source (Example): Investopedia: Amortization | Khan Academy
Variables Explained
The calculation requires three primary inputs:
- Loan Principal ($P$): The initial amount borrowed from the lender. This does not include any down payment.
- Annual Interest Rate ($R$): The yearly percentage rate charged on the principal. This is converted to a monthly rate for calculation.
- Loan Term (Years, $N$): The length of time over which the loan will be repaid, usually 15 or 30 years.
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What is a Mortgage Payment Calculator?
A mortgage payment calculator is a critical financial tool that uses the loan’s principal amount, interest rate, and repayment term to estimate the fixed monthly amount a borrower must pay to fully amortize the loan. It is essential for pre-qualification planning and determining a comfortable budget.
The calculated monthly payment includes both the repayment of the principal and the interest accrued on the outstanding balance. It typically does not include escrow items like property taxes or homeowner’s insurance, which must be factored in separately for the total housing cost.
How to Calculate Mortgage Payment (Example)
Let’s calculate the monthly payment for a $200,000 loan at a 5% annual rate over 30 years.
- Convert Annual Rate to Monthly Rate ($i$): $5\% / 12 / 100 = 0.0041667$.
- Calculate Total Number of Payments ($n$): $30 \text{ years} \times 12 \text{ months/year} = 360$ payments.
- Calculate Factor $(1+i)^n$: $(1 + 0.0041667)^{360} \approx 4.4677$.
- Apply Amortization Formula: $M = 200,000 \times \left[ \frac{0.0041667 \times 4.4677}{4.4677 – 1} \right]$.
- Solve for M: $M \approx 200,000 \times 0.005368 \approx \$1,073.64$.
Frequently Asked Questions (FAQ)
Is the calculated payment my final cost?
No. The calculated figure is the principal and interest (P&I) portion only. Your total monthly payment often includes escrowed amounts for property taxes, homeowner’s insurance, and private mortgage insurance (PMI), making the final payment higher.
How does increasing the term (years) affect my payment?
A longer term (e.g., 30 years vs. 15 years) reduces the monthly payment because the principal is spread out over more periods. However, it significantly increases the total amount of interest paid over the life of the loan.
What is the difference between APR and Interest Rate?
The Interest Rate is the annual cost of the principal. The Annual Percentage Rate (APR) includes the interest rate plus other costs, such as lender fees, points, and mortgage insurance, giving a more comprehensive measure of the loan’s total cost.
What is amortization?
Amortization is the process of gradually paying off a debt over a fixed period of time with a set schedule of payments. In a typical mortgage, early payments are mostly interest, and later payments are mostly principal.