How to Calculate Your Mortgage Payment by Hand (Formula + Example)

Every mortgage payment hides the same piece of arithmetic, and once you see it, the lender's quote stops being a black box. The number on your loan estimate isn't magic — it's a single closed-form equation that anyone can run with a calculator that has an exponent key. This guide shows you the formula, walks one realistic loan through it step by step with verified numbers, and then explains why the payment you actually mail every month is bigger than what the formula gives you.

Estimates for education only — not financial advice. The math here is exact, but real mortgages add taxes, insurance, fees, and rounding rules that vary by lender and jurisdiction. Confirm any number with your lender or a licensed professional before making a decision.

TL;DR: what's the formula?

The fixed-rate mortgage payment is:

        P · [ r(1 + r)^n ]
M  =  ─────────────────────
         (1 + r)^n − 1

where:

• M = the monthly payment (principal + interest only)
• P = the principal — the amount you borrow
• r = the monthly interest rate = annual rate ÷ 12 (as a decimal)
• n = the total number of payments = years × 12

For a $300,000 loan at 6.5% for 30 years, that works out to M ≈ $1,896.20 per month. The two steps people get wrong: dividing the annual rate by 12 to get r, and using the number of payments (360, not 30) for n. Everything below is detail. To skip the arithmetic entirely, the mortgage calculator does this exact formula instantly in your browser.

What does each variable mean?

The formula is the standard amortization equation — it's the same one the U.S. Consumer Financial Protection Bureau and Freddie Mac describe for any fully-amortizing fixed-rate loan. Each input has a precise definition that trips people up:

• P (principal) is the loan balance after your down payment, not the home price. Buy a $375,000 house with $75,000 down and P = $300,000.
• r (monthly rate) is the annual interest rate divided by 12, written as a decimal. A 6.5% loan has an annual decimal rate of 0.065, so r = 0.065 / 12 = 0.00541666…. This is the interest rate, not the APR — more on that distinction below.
• n (number of payments) is the loan term in months. A 30-year loan is 30 × 12 = 360 payments; a 15-year loan is 180.

The (1 + r)^n term is compound growth: it's what $1 of debt becomes after n months of monthly compounding. If compounding interest is new to you, the compound interest calculator shows the same (1 + r)^n engine working on savings instead of debt.

How do you calculate a mortgage payment step by step?

Work the formula in four steps, never skipping the order of operations. Compute r, then (1 + r)^n, then assemble the numerator and denominator, then divide and multiply by P. Here is a $300,000 loan at a 6.5% annual rate over 30 years, computed exactly.

Step 1 — Find the monthly rate r.

r = 0.065 / 12 = 0.0054166666…  (≈ 0.0054167)

Step 2 — Find the number of payments n.

n = 30 years × 12 months = 360

Step 3 — Compute the compounding factor (1 + r)^n.

(1 + r)^n = (1.0054166…)^360 = 6.9917979…

This is the one step that needs an exponent key (y^x or ^ on most calculators). Raising 1.0054167 to the 360th power gives about 6.99180.

Step 4 — Assemble and divide.

Numerator   = P · [ r · (1 + r)^n ]
            = 300,000 · (0.0054167 · 6.99180)
            = 300,000 · 0.0378722
            = 11,361.67

Denominator = (1 + r)^n − 1
            = 6.99180 − 1
            = 5.99180

M = 11,361.67 / 5.99180 = 1,896.20

So M ≈ $1,896.20 per month in principal and interest. (Computed with full precision, the exact figure is $1,896.2041; lenders round to the cent.) Plug the same inputs into the mortgage calculator to confirm it, or use the more general loan calculator for car loans and personal loans that use the identical formula.

Why is my real payment bigger than M? (PITI explained)

The formula gives you principal and interest only. Your actual monthly housing payment is PITI — and lenders escrow most of it on top of M. PITI stands for:

• P — Principal: the slice that pays down your loan balance.
• I — Interest: the lender's charge on the outstanding balance.
• T — Taxes: property taxes, collected monthly into an escrow account and paid to your local government once or twice a year.
• I — Insurance: homeowners (hazard) insurance, also escrowed.

Two more line items appear for many borrowers:

• PMI (private mortgage insurance): required by most lenders when your down payment is under 20%, per the CFPB's explainer on PMI. It protects the lender, not you, and typically runs 0.5%–1.5% of the loan per year.
• HOA dues: if the property is in a homeowners association, those fees stack on top — though they're usually paid directly, not escrowed.

On our $300,000 example, the formula payment is $1,896.20. Add, say, $400/month in property taxes, $120 in homeowners insurance, and $150 in PMI, and the check you actually write is closer to $2,566 — about 35% more than the formula alone suggests. Always budget PITI, never bare M.

How does amortization work — and how much interest do you really pay?

Amortization means each payment is split between interest and principal, and the early payments are almost all interest. The interest portion of any month is just balance × r; whatever's left of M goes to principal. As the balance shrinks, the interest slice shrinks and the principal slice grows — slowly at first, then faster near the end.

On the first payment of our example loan:

Interest  = balance × r = 300,000 × 0.0054167 = 1,625.00
Principal = M − interest = 1,896.20 − 1,625.00 =   271.20

Of your very first $1,896.20, only $271.20 actually reduces the debt — the other $1,625.00 is pure interest. That ratio is why paying a little extra toward principal early has an outsized effect: every dollar of extra principal skips all the future interest it would have accrued.

Over the full life of the loan, the total cost is stark:

Total paid     = M × n = 1,896.20 × 360 = 682,633.47
Total interest = total paid − P = 682,633.47 − 300,000 = 382,633.47

You borrow $300,000 and repay $682,633 — meaning $382,633 of interest, more than the house's loan amount itself. Seeing that number is the strongest argument for a shorter term or extra principal payments.

How much does the rate or term change the payment?

The payment is extremely sensitive to both the interest rate and the term. The tables below hold the $300,000 principal constant and vary one factor at a time. All figures are computed with the formula above and rounded to the cent.

Same 30-year term, different rates:

| Annual rate | Monthly payment (M) | Total interest over 30 yrs | |-------------|--------------------|----------------------------| | 5.5% | $1,703.37 | $313,212 | | 6.5% | $1,896.20 | $382,633 | | 7.5% | $2,097.64 | $455,152 |

A two-point swing in rate — 5.5% to 7.5% — adds about $394/month and nearly $142,000 in lifetime interest on the same loan. Rate matters more than almost any other lever. To explore "what if" rate scenarios, the percentage calculator helps with the rate-difference math.

Same 6.5% rate, 15-year vs 30-year term:

| Term | Monthly payment (M) | Total paid | Total interest | |------|--------------------|------------|----------------| | 15 years (n = 180) | $2,613.32 | $470,398 | $170,398 | | 30 years (n = 360) | $1,896.20 | $682,633 | $382,633 |

The 15-year payment is about $717/month higher, but it saves roughly $212,000 in interest because you're borrowing the money for half as long. The shorter term costs more per month and far less overall — the classic mortgage trade-off.

What are the most common mistakes?

Almost every wrong mortgage estimate comes from one of these three errors:

1. Confusing the interest rate with the APR. The interest rate is what the formula uses. The APR (annual percentage rate) is a broader figure mandated by the federal Truth in Lending Act — it folds in points, lender fees, and mortgage insurance, so it's almost always higher than the note rate. The CFPB explains the difference here. Plug the APR into the payment formula and you'll overstate your monthly payment.
2. Forgetting to divide the annual rate by 12. The formula needs the monthly rate. Using r = 0.065 instead of 0.065 / 12 inflates the payment to absurd levels. Likewise, n is in months (360), not years (30).
3. Quoting bare M as the "payment." Skipping taxes, insurance, and PMI undersells the true monthly cost — often by 25%–40%. Budget PITI, not principal-and-interest.

A good sanity check: a 30-year payment should be roughly $6 to $7 per $1,000 borrowed at typical rates. Our $300K loan at $1,896 is about $6.32 per $1,000 — right in range. If your hand calculation lands far outside that, you've likely mishandled r or n.

TL;DR

A fixed mortgage payment is one formula: M = P · [r(1 + r)^n] / [(1 + r)^n − 1], where P is the amount borrowed, r is the annual rate ÷ 12, and n is years × 12. For $300,000 at 6.5% over 30 years, r = 0.0054167, n = 360, (1 + r)^n ≈ 6.9918, and M ≈ $1,896.20/month — but over the full term you repay about $682,633, of which $382,633 is interest. Your real check is larger still, because the true monthly cost is PITI (principal, interest, taxes, insurance) plus PMI and HOA where they apply. The three errors to avoid: confusing the interest rate with the higher APR, forgetting to divide the annual rate by 12, and quoting bare principal-and-interest as the "payment."

Run your own numbers with the mortgage calculator, compare loan structures in the loan calculator, model the compounding with the compound interest calculator, or browse every free, in-browser utility in the tools directory. For authoritative guidance, see the CFPB's mortgage resources, Freddie Mac's homebuying tools, and the SEC's investor.gov compound interest material. Estimates for education only — not financial advice.