Understanding your mortgage results
The following reference thresholds are used by lenders and consumer finance agencies to assess mortgage affordability. They are guidelines, not hard limits.
| Ratio | Guideline (CFPB / conventional lenders) |
|---|---|
| Housing cost / gross income | ≤ 28% (front-end ratio) — conventional benchmark |
| All debt / gross income | ≤ 36% (back-end ratio) — conventional benchmark |
| Down payment | < 20% typically requires private mortgage insurance (PMI) |
| Loan-to-value (LTV) | ≤ 80% avoids PMI on conventional loans |
- This calculator does not include property taxes, homeowner's insurance, HOA fees, or private mortgage insurance (PMI). Adding these can increase the true monthly housing cost by hundreds of dollars.
- The interest rate input should be the mortgage note rate (the nominal rate on the loan agreement), not the APR. The APR includes fees and is typically slightly higher.
- Adjustable-rate mortgages (ARMs) start with a fixed rate for an initial period (e.g., 5 years), then adjust periodically. This calculator models only fixed-rate mortgages.
- Paying extra each month toward principal reduces the remaining balance and total interest paid. The fixed payment shown here does not incorporate prepayments.
What is a mortgage calculator?
A mortgage calculator applies the standard loan amortization formula to determine the fixed monthly payment required to repay a home loan — principal plus interest — in equal installments over a specified term. Most conventional mortgages in the United States and United Kingdom are fully amortizing, meaning each payment covers accrued interest for that month and a portion of the outstanding principal, so the balance reaches exactly zero at the end of the term.
The calculator derives the loan principal from the home price minus the down payment. It then computes the monthly payment at the stated annual interest rate, and shows the cumulative cost over the loan's life: total amount paid and total interest, which is the difference between cumulative payments and the original principal.
The Consumer Financial Protection Bureau (CFPB) publishes the 28/36 affordability rule as a common lender guideline: housing expenses (mortgage principal, interest, taxes, and insurance) should not exceed 28% of gross monthly income, and total debt payments should not exceed 36% of gross monthly income. This calculator reports the payment; users should verify affordability against their own income using those thresholds.
How to use this mortgage calculator
- Enter the home purchase price and your planned down payment. The calculator derives the loan principal (price minus down payment).
- Enter the annual interest rate offered by your lender. This is the nominal rate, not the APR (which includes fees).
- Enter the loan term in years. Common terms are 15 and 30 years in the United States.
- Read the fixed monthly payment, the total amount you will pay over the full term, and the total interest cost.
- Apply the 28% rule: divide the monthly payment by your gross monthly income. If the result exceeds 0.28, the payment may be considered high relative to income by conventional lender standards.
The amortization formula
The fixed monthly payment M is derived from the present-value annuity formula, which sets the present value of all future monthly payments equal to the loan principal P. The monthly interest rate r equals the annual rate divided by 12; n is the total number of monthly payments (years × 12).
When the interest rate is zero, the formula simplifies to M = P/n (principal divided by number of payments), which is a special case handled separately.
Frequently asked questions
How is a monthly mortgage payment calculated?
A fixed-rate mortgage payment is calculated using the amortization formula M = P·[r(1+r)^n]/[(1+r)^n−1], where P is the loan principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. Each payment is the same amount; the proportion that goes to interest decreases over time as the principal balance falls.
What is the 28/36 rule?
The 28/36 rule is a conventional lender and consumer finance guideline stating that a borrower's monthly housing costs (principal, interest, taxes, and insurance) should not exceed 28% of gross monthly income (the front-end ratio), and total monthly debt payments should not exceed 36% of gross monthly income (the back-end ratio). The Consumer Financial Protection Bureau (CFPB) cites this rule as a common affordability benchmark.
How much does a 30-year versus 15-year mortgage cost?
A 15-year mortgage typically carries a lower interest rate than a 30-year mortgage and eliminates principal in half the time, substantially reducing total interest paid. However, the monthly payment is significantly higher because the same principal is repaid in half as many installments. The choice involves a trade-off between monthly cash flow and total lifetime interest cost.
What is PMI and when is it required?
Private mortgage insurance (PMI) is a policy that protects lenders when a borrower makes a down payment of less than 20% of the home's purchase price on a conventional loan. PMI is typically added to the monthly mortgage payment and ranges from approximately 0.5% to 1.5% of the loan amount per year, depending on the lender, loan type, and credit score. This calculator does not include PMI.
Does paying extra toward principal save money?
Yes. Making additional payments directed to the principal balance reduces the outstanding loan amount faster, which decreases the total interest that accrues over the life of the loan and shortens the payoff period. Even a modest extra payment each month can save a significant amount in total interest on a 30-year mortgage.
What is the difference between interest rate and APR?
The interest rate (or note rate) is the cost of borrowing the principal expressed as an annual percentage, used to calculate the monthly payment. The Annual Percentage Rate (APR) includes the interest rate plus lender fees, discount points, and certain closing costs, expressed as a yearly rate. APR gives a more complete picture of borrowing cost and is typically slightly higher than the note rate.
References
- Consumer Financial Protection Bureau (CFPB). Debt-to-income calculator and affordability guidance. consumerfinance.gov.
- Federal Reserve Board. A consumer's guide to mortgage refinancing. federalreserve.gov.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Chapter 2: How to Calculate Present Values.
- US Department of Housing and Urban Development (HUD). Buying a home: what you need to know. hud.gov.
- Freddie Mac. Understanding mortgage options and loan types. freddiemac.com.