How to Calculate a Mortgage Payment by Hand and
The amortization formula, step by step, plus how taxes and insurance change the real payment. Worked example for a $300,000 loan at 6.5%.
By The RateFig Editorial Team · July 30, 2026 · reviewed against official mortgage and rate sources
You do not need to compute your mortgage payment by hand to buy a home, but understanding the formula removes the mystery — and helps you sanity-check any quote. This guide shows the math, then explains why the real payment is usually larger than the formula's answer.
The Amortization Formula
For a level-payment, fully amortizing loan:
M = P × [ r(1+r)ⁿ ] / [ (1+r)ⁿ − 1 ]
- M = monthly principal-and-interest payment
- P = loan principal (amount borrowed)
- r = monthly interest rate = annual rate ÷ 12
- n = number of payments = years × 12
Worked Example, Step by Step
Loan: $300,000 at 6.50% for 30 years.
- r = 0.065 ÷ 12 = 0.0054167
- n = 30 × 12 = 360
- (1+r)ⁿ = (1.0054167)³⁶⁰ ≈ 6.992
- Numerator: r × (1+r)ⁿ = 0.0054167 × 6.992 ≈ 0.037872
- Denominator: (1+r)ⁿ − 1 = 6.992 − 1 = 5.992
- Factor: 0.037872 ÷ 5.992 ≈ 0.006320
- M = 300,000 × 0.006320 ≈ $1,896
So the monthly principal and interest is about $1,896. Over 360 payments you pay roughly $682,600 total, of which about $382,600 is interest.
Why the Real Payment Is Bigger: PITI
The formula gives P&I only. Most borrowers also pay into escrow each month for:
- Property taxes — set by the county; varies widely by location.
- Homeowners insurance — required by the lender.
- Mortgage insurance — if your down payment is below 20% (conventional) or on FHA loans.
Example with escrow
| Component | Monthly | |-----------|---------| | Principal & interest | $1,896 | | Property taxes (est. 1.1%/yr on value) | ~$275 | | Homeowners insurance (est.) | ~$100 | | Mortgage insurance (if <20% down) | ~$130 | | Total housing payment | ~$2,400 |
Two loans with the same rate can have very different total payments purely because of taxes and insurance.
What Changes the Payment Most
- Rate. A 0.25-point drop on this loan saves about $45–50/month.
- Term. A 15-year term at the same rate raises the payment but cuts total interest sharply.
- Loan amount. Larger balance, larger payment, roughly linearly.
Checking a Quote
When a lender quotes you, separate the P&I (from the formula) from the escrow and fees. If the P&I does not match the formula at your rate and term, ask why. And remember the APR — not the note rate — is what includes the upfront costs, which the monthly P&I never shows.
The Practical Move
Use the calculator to test scenarios before you shop: different rates, terms, down payments, and tax/insurance estimates for the homes you are considering. Walking into a Loan Estimate already knowing the right P&I for your inputs makes an expensive quote obvious immediately.
All calculations are approximate for planning purposes only. This article does not provide official financial, legal, or tax advice. Verify any decision with a qualified mortgage lender or financial advisor.
Frequently Asked Questions
What is the mortgage payment formula?+
M = P × [ r(1+r)^n ] / [ (1+r)^n − 1 ], where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments (years × 12).
Does the formula include taxes and insurance?+
No. It returns principal and interest only. The full housing payment adds property taxes, homeowners insurance, and any mortgage insurance held in escrow.
Why do my early payments barely reduce the balance?+
Because interest is charged on the remaining balance. Early on the balance is largest, so most of each payment is interest; the principal share grows as the balance falls.
Where can I calculate it without doing the math?+
Use the free calculator at /tools/mortgage-calculator/. It runs the same US-standard formula in real time, no signup required, and adds taxes and insurance if you enter them.
Run the Numbers Yourself
Reading is the first step. The next is plugging your own numbers into a calculator that runs the same US-standard formulas in real time — no signup, no paywall, instant results.
Open the calculator→Key Takeaways
Use the calculator linked above to confirm how these concepts apply to your specific loan amount, rate, and term. Small changes in any one input can shift your monthly payment and total interest by thousands of dollars over the life of the loan.
Continue Learning
- Mortgage BasicsWhat Is PITI? Breaking Down Principal, Interest, Taxes, and Insurance
- Mortgage BasicsMortgage Principal vs Interest: What Each Dollar Actually Does
- Calculator TutorialsWhat Is an Amortization Schedule? How to Read Your Mortgage Breakdown
- Mortgage PaymentsMonthly Mortgage Payment Breakdown: Where Every Dollar Goes