How to calculate mortgage payments by hand (with amortization)

Learning how to calculate mortgage payments by hand is easier than it looks: one formula, three inputs, and about two minutes with a basic calculator. Below is the exact formula lenders use, three fully worked examples — a 30-year, a 15-year and a 20-year loan — and a look at how each payment splits between principal and interest, so you can check any loan offer against your own math before you sign.

The mortgage payment formula

Every fixed-rate mortgage payment in the United States comes from the same equation:

• M is the monthly payment you are solving for.
• P is the principal — the amount you borrow.
• r is the monthly interest rate: the annual rate divided by 12. On a 6.5% loan, r = 0.065 ÷ 12 = 0.0054167.
• n is the number of monthly payments: the term in years × 12. A 30-year loan has n = 360.

The formula finds the one payment that, repeated n times, exactly retires the loan: each month it covers that month’s interest plus a slice of principal, and the final payment brings the balance to exactly $0. One caution before the examples: this payment is principal and interest only. Property taxes, homeowners insurance and private mortgage insurance are added on top by your lender, which is why the monthly total on a Loan Estimate is higher than the number this formula produces — the Consumer Financial Protection Bureau (CFPB) requires lenders to itemize those extras separately.

Worked example 1: $350,000 at 6.5% for 30 years

Step 1 — convert the inputs. r = 0.065 ÷ 12 = 0.0054167, and n = 30 × 12 = 360.

Step 2 — grow the rate factor. (1 + r)ⁿ = (1.0054167)³⁶⁰ = 6.9918. This is the hardest step on a basic calculator; the exponent key (xʸ) handles it in one press.

Step 3 — multiply principal by the rate. P × r = $350,000 × 0.0054167 = $1,895.83. Hold on to this number: it is also the interest charged in month one.

Step 4 — build the denominator. 1 − (1 + r)⁻ⁿ = 1 − (1 ÷ 6.9918) = 1 − 0.143025 = 0.856975.

Step 5 — divide. M = $1,895.83 ÷ 0.856975 = $2,212.24 per month.

Now check the answer against the first rows of the amortization schedule it creates. Interest each month is the balance × r; whatever is left of the payment reduces the balance:

First three payments on a $350,000 loan at 6.5%. Interest shrinks — and principal grows — by roughly $1.70 a month at first, then faster as the balance falls.

Run the schedule all the way out and the totals are sobering: over 360 payments you hand over $796,404.05, of which $446,404.05 is interest — more than the $350,000 you borrowed. (The very last payment is $2,209.89 rather than $2,212.24, because each month’s interest is rounded to the nearest cent and the final payment trues up the difference.)

Worked example 2: $250,000 at 5% for 15 years

Same five steps, faster. r = 0.05 ÷ 12 = 0.0041667 and n = 15 × 12 = 180. Then (1 + r)ⁿ = 2.1137, P × r = $250,000 × 0.0041667 = $1,041.67, and the denominator is 1 − (1 ÷ 2.1137) = 1 − 0.473103 = 0.526897. So M = $1,041.67 ÷ 0.526897 = $1,976.98 per month.

Look at the very first payment: interest is $1,041.67 and principal is $935.31, leaving a balance of $249,064.69. Nearly half the payment is principal from day one — compare example 1, where principal was just $316.41 of a $2,212.24 payment, about 14%. The 15-year loan’s total interest is $105,857.58 on $355,857.58 of total payments.

Worked example 3: $180,000 at 4.5% for 20 years

r = 0.045 ÷ 12 = 0.00375 and n = 20 × 12 = 240. Then (1 + r)ⁿ = 2.4555, P × r = $180,000 × 0.00375 = $675.00, and the denominator is 1 − (1 ÷ 2.4555) = 1 − 0.407255 = 0.592745. So M = $675.00 ÷ 0.592745 = $1,138.77 per month.

Month one charges $675.00 of interest and pays down $463.77 of principal, for a balance of $179,536.23. Across the whole loan you pay $273,304.32, of which $93,304.32 is interest.

The three examples side by side

All totals come from cent-exact amortization schedules; the final payment of each loan is adjusted by a few cents for rounding.

The pattern to notice: the payment scales with the amount and the rate, but total interest scales with the term. Example 1 borrows 40% more money than example 2, yet pays over four times as much interest — $446,404.05 against $105,857.58 — purely because it takes twice as long to pay back.

From one payment to the whole schedule

Once you have M, the rest of amortization is simple repetition. For every month: interest = current balance × r; principal = M − interest; new balance = old balance − principal. Repeat 360 times and you have the full schedule — which is exactly what our Amortization Calculator generates instantly, and what the Mortgage Calculator uses when it compares loan sizes side by side.

Why the by-hand answer is worth having

Two minutes of arithmetic buys you something no calculator alone can: a sanity check. When a lender quotes a payment, when a Loan Estimate lands in your inbox, when an online tool gives you a number that feels off — you can now rebuild that number from the loan amount, the rate and the term, and see whether it survives. If your by-hand result matches, you understand exactly what you are being charged for. If it does not match, the difference is almost always something added on top — taxes, insurance, or fees — and you know precisely what to ask about before signing.

Sources: Consumer Financial Protection Bureau (CFPB) guidance on the Loan Estimate and shopping for a mortgage; standard amortization mathematics. Every worked example and schedule figure in this article was recomputed cent by cent.