Use this tool to quickly calculate your monthly mortgage payment, total interest, and the amortization schedule for your loan.
Mortgage Calculation
Estimated Monthly Payment
Total Interest Paid:
Detailed Calculation Breakdown
Mortgage Calculation Formula
Where:
Variables
- M: Monthly payment (the variable being solved for).
- P: Principal Loan Amount (The initial amount borrowed).
- i: Monthly interest rate (The annual rate divided by 12 and 100).
- n: Total number of payments (The loan term in years multiplied by 12).
Related Calculators
Explore other financial tools for your planning needs:
- Amortization Schedule Calculator
- Home Affordability Calculator
- Refinance Break-Even Calculator
- Early Mortgage Payoff Calculator
What is Mortgage Calculation?
A mortgage calculation determines the size of the periodic payments (usually monthly) required to fully repay a loan, including both principal and interest, over a specified loan term. This process uses the time value of money to ensure that the outstanding principal balance is reduced to zero by the end of the loan term.
The calculation is critical for budgeting, as the monthly payment (P&I) is often the largest component of homeownership costs. It allows prospective homeowners to understand their long-term financial commitment and compare different loan products (e.g., 15-year vs. 30-year mortgages).
How to Calculate Mortgage Calculation (Example)
Let’s use an example: Principal $300,000, Annual Rate 6.0%, Term 30 Years.
- Determine Monthly Rate (i): Divide the annual rate by 1200. $6.0\% / 1200 = 0.005$.
- Determine Total Payments (n): Multiply the term by 12. $30 \text{ years} \times 12 = 360 \text{ payments}$.
- Calculate the Factor: Calculate the term $\left[\frac{i(1 + i)^n}{(1 + i)^n – 1}\right]$. Using the numbers: $\left[\frac{0.005(1.005)^{360}}{(1.005)^{360} – 1}\right] \approx 0.0059955$.
- Calculate Monthly Payment (M): Multiply the principal by the factor. $300,000 \times 0.0059955 \approx \$1,798.65$.
- Calculate Total Interest: $\left(M \times n\right) – P$. $(\$1,798.65 \times 360) – \$300,000 \approx \$347,514$.
Frequently Asked Questions (FAQ)
No, the standard mortgage calculation only computes the Principal and Interest (P&I) portion. Taxes and insurance (known as PITI) are often bundled into your monthly payment via an escrow account, but are separate from the loan amortization formula.
What happens if the interest rate changes?If you have a Fixed-Rate Mortgage (FRM), the rate and monthly payment remain constant. If you have an Adjustable-Rate Mortgage (ARM), the rate and payment will change periodically based on a benchmark index after the initial fixed period.
Is it better to take a 15-year or 30-year mortgage?A 15-year mortgage typically has a lower interest rate and saves substantial money on total interest, but requires a significantly higher monthly payment. A 30-year mortgage offers lower monthly payments and more financial flexibility, but costs much more over the life of the loan.
How does making extra payments affect the calculation?Making extra principal payments shortens the life of the loan and significantly reduces the total interest paid. The monthly payment remains the same, but more of it goes toward principal, accelerating the payoff date.