Mortgage Calculator
A mortgage payment is the fixed monthly amount that repays a home loan, calculated from the principal, interest rate, and term with the amortization formula M = P[r(1+r)^n] / [(1+r)^n - 1]. This calculator estimates your total monthly payment — including property taxes, homeowners insurance, and PMI — and builds a full amortization schedule.
Mortgage Calculator
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Formula: M = P[r(1+r)^n] / [(1+r)^n - 1]
Worked example — Monthly Payment: $2,162 | Total Interest: $357,143 | Total Cost: $777,943
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor · Editorial policy
How is a mortgage payment calculated?
M = P[r(1+r)^n] / [(1+r)^n - 1]
Where M = Monthly payment (principal & interest), P = Loan principal (home price minus down payment), r = Monthly interest rate (annual rate / 12), n = Total number of payments (years x 12). Total monthly payment also includes property tax, homeowner's insurance, and PMI if applicable.
How do you calculate a mortgage payment step by step?
Example 1: Standard 30-Year Mortgage
Problem:You're buying a $350,000 home with 20% down ($70,000), 30-year fixed at 6.5%, property taxes of $3,500/year, and insurance of $1,200/year.
Solution:Loan amount = $350,000 - $70,000 = $280,000 Monthly rate = 6.5% / 12 = 0.5417% Monthly P&I = $280,000 x [0.005417 x (1.005417)^360] / [(1.005417)^360 - 1] = $1,769.84 Monthly tax = $3,500 / 12 = $291.67 Monthly insurance = $1,200 / 12 = $100.00 PMI = $0 (20% down) Total monthly = $2,161.51
Result:Monthly Payment: $2,162 | Total Interest: $357,143 | Total Cost: $777,943
Example 2: Low Down Payment with PMI
Problem:You're buying a $300,000 home with 5% down ($15,000), 30-year fixed at 7%, property taxes of $3,000/year, and insurance of $1,100/year.
Solution:Loan amount = $300,000 - $15,000 = $285,000 Monthly P&I = $285,000 x [0.005833 x (1.005833)^360] / [(1.005833)^360 - 1] = $1,896.07 Monthly tax = $3,000 / 12 = $250 Monthly insurance = $1,100 / 12 = $91.67 PMI = $285,000 x 0.5% / 12 = $118.75 Total monthly = $2,356.49
Result:Monthly Payment: $2,356 | Total Interest: $397,585 | PMI adds $119/month
What else do people ask about mortgage payments?
How is a monthly mortgage payment calculated?
A monthly mortgage payment is calculated using an amortization formula that considers the loan principal, interest rate, and loan term. The formula is M = P[r(1+r)^n]/[(1+r)^n-1], where M is the monthly payment, P is the loan principal, r is the monthly interest rate, and n is the total number of payments. Your total monthly housing payment also includes property taxes divided by 12, homeowner's insurance divided by 12, and possibly private mortgage insurance (PMI) if your down payment is less than 20%. In the early years of your mortgage, most of your payment goes toward interest. As time passes, more of each payment goes toward the principal balance. This is called amortization.
What is PMI and when is it required?
Private Mortgage Insurance (PMI) is required by lenders when your down payment is less than 20% of the home's purchase price. PMI protects the lender, not you, in case you default on the loan. PMI typically costs between 0.3% and 1.5% of the original loan amount per year. For a $300,000 loan, that's about $75 to $375 per month. PMI is automatically removed once your loan-to-value ratio reaches 78% through regular payments, or you can request removal at 80% LTV.
Should I choose a 15-year or 30-year mortgage?
A 15-year mortgage has higher monthly payments but saves significantly on total interest. A 30-year mortgage has lower monthly payments but costs more over the life of the loan. On a $300,000 loan at 6.5%, the 15-year option saves a large amount of interest but requires a much higher monthly payment. Choose the 30-year if you need payment flexibility. Choose the 15-year if you can comfortably afford the higher payment and want to build equity faster.
How does the down payment affect my mortgage?
The down payment directly affects your loan amount, monthly payment, interest paid, and whether you need PMI. A larger down payment means borrowing less, paying less interest, and having lower monthly payments. With a $350,000 home at 6.5% for 30 years: 5% down ($17,500) gives a monthly P&I of $2,101 plus PMI. 10% down ($35,000) gives $1,990/month plus PMI. 20% down ($70,000) gives $1,769/month with no PMI. The 20% down payment option saves roughly $332/month compared to 5% down. Over 30 years, the difference in total interest paid is over $100,000. However, tying up too much cash in a down payment can leave you without an emergency fund, so balance is important.
What other costs should I budget for when buying a home?
Beyond your monthly mortgage payment, budget for closing costs (typically 2-5% of the loan amount), which include appraisal fees, title insurance, origination fees, and attorney fees. Ongoing costs include property taxes (typically 0.5-2.5% of home value annually), homeowner's insurance ($1,000-$3,000/year), HOA fees if applicable ($200-$500/month), maintenance and repairs (budget 1-2% of home value annually), and utilities. You should also maintain an emergency fund covering 3-6 months of housing expenses. Many first-time buyers underestimate these costs. A good rule of thumb is that your total monthly housing expense should not exceed 28% of your gross monthly income, and total debt payments should not exceed 36%. This is known as the 28/36 rule.
What does PITI include beyond principal and interest?
The formula M = P[r(1+r)^n]/[(1+r)^n-1] produces only principal and interest. PITI adds the property tax and homeowner insurance instalments collected each month, and lenders also fold in mortgage insurance and any HOA dues when assessing affordability. On a modest loan in a high-tax county the tax and insurance portion can rival the interest portion, so comparing a bare P and I figure against a rent quote systematically understates the cost of owning.
How does an escrow account work and why does my payment change?
The servicer collects a twelfth of the estimated annual tax and insurance bills with each payment, holds them in escrow, and pays the bills when due. Once a year it runs an escrow analysis: if assessments or premiums rose, the monthly collection increases and any shortfall is spread over the following year or billed as a lump sum. This is why a fixed-rate mortgage payment can still rise even though the principal and interest component never moves.
What is the trade-off between paying discount points and accepting a higher rate?
One discount point costs 1% of the loan amount and buys the note rate down by a lender-specific increment. Divide the point cost by the monthly payment saving to get the break-even in months, then pay the points only if you expect to hold the loan well past that date. A lender credit is the mirror trade, covering closing costs in exchange for a higher rate, which suits borrowers short on cash or likely to move or refinance soon.
Why is nearly all of an early mortgage payment interest?
Interest each month is the remaining balance multiplied by the monthly rate, and in the first years that balance is close to the full principal. At typical thirty-year rates the interest charge consumes most of the fixed payment, leaving only a small residue to reduce the balance. As the balance falls the interest charge falls with it and the principal share accelerates, which is why the amortisation schedule crosses over well past the loan midpoint.
How does the loan-to-value ratio influence the interest rate a lender quotes?
Loan-to-value is the loan amount divided by the appraised value or the purchase price, whichever is lower, and lenders price risk in tiers against it: a borrower at a lower LTV generally sees a better rate or fewer pricing adjustments than an otherwise identical borrower at a high LTV. Combined LTV adds any second lien, such as a home equity line, and governs cash-out and piggyback structures. Because the figure depends on the appraisal, a low appraisal can drop you into a worse pricing tier than expected.
References
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