How to Calculate Mortgage Payments by Hand (Formula + Examples)

What is the mortgage payment formula?

A mortgage is an amortizing loan. That is the technical term for a simple idea: you make one fixed payment every month, and that payment is sized so the loan is paid off to the penny after n payments, interest included. The formula that produces that magic number is:

Each letter has a plain meaning. P is the principal, the amount you actually borrow (home price minus down payment). r is the monthly interest rate, which is your annual rate divided by 12. n is the total number of monthly payments: 360 for a 30-year loan, 180 for a 15-year. M is the answer, your fixed monthly principal-and-interest payment.

Why does the formula look so strange? Think of it as a balancing act. Every month the bank charges interest on whatever balance remains, and your fixed payment covers that interest plus a slice of principal. Early on, interest eats most of the payment because the balance is huge. Over time the principal slice grows. The formula finds the single monthly number where this process lands exactly on zero after n months. No more, no less.

My recommendation: learn r and n before anything else, because 90% of hand-calculation errors come from getting those two wrong. People divide by the wrong thing, forget the monthly conversion, or use years where months belong. Get r and n right and the rest is just button pushing.

How do you work through the formula step by step?

Take a concrete loan: $300,000 borrowed at 6.5% APR for 30 years. Grab any scientific calculator (the one on your phone has a y^x key if you rotate it sideways).

Step 1: Find r, the monthly rate. Divide the annual rate by 12. That gives 0.065 / 12 = 0.00541667. Never use 6.5 in the formula; always the decimal form, and always monthly.

Step 2: Find n, the number of payments. 30 years × 12 = 360 monthly payments.

Step 3: Raise (1 + r) to the power of n. Compute (1.00541667)^360 = 6.991798. This is the compound-growth factor: the same math that makes savings grow also makes loan balances grow before payments knock them down.

Step 4: Build the numerator and denominator. Numerator = r × 6.991798 = 0.037873. Denominator = 6.991798 − 1 = 5.991798.

Step 5: Divide and multiply by P. 0.037873 / 5.991798 = 0.0063207. Multiply by $300,000 and you get $1,896.20 per month.

That is the principal-and-interest portion of the payment, fixed for the life of the loan. Over 360 payments you will send the bank $682,632 total, which means $382,632 in interest on a $300,000 loan. Seeing that number in the open is the single most convincing argument for making extra payments, which we will get to below.

Why is the first payment almost all interest?

Here is the payment split for month one of that same loan. The interest charge is the balance ($300,000) times the monthly rate (0.00541667), which equals $1,625.00. Subtract that from the $1,896.20 payment and only $271.20 pays down the principal. The bank takes its interest first, every month, and whatever is left chips away at the balance.

This is why the payoff feels slow at the start. After 10 full years of payments (120 months), the balance is still about $254,329. You have paid over $227,000 and barely dented the principal. After 20 years (240 months), the balance is down to roughly $166,998, and by then the split has flipped: most of each payment is principal.

The practical lesson is blunt. Extra money matters most at the beginning of the loan, when nearly every extra dollar avoids future interest. An extra $200 in year one kills far more total interest than the same $200 in year 25, when the balance is already small. If you are going to prepay, start early.

What does the formula leave out?

The formula answers one question: how much goes to the lender for principal and interest? But the check you actually write is bigger. Four more costs pile on top, and together they surprise almost every first-time buyer.

Property tax. Your county bills you annually, and the lender collects one-twelfth of it each month into escrow. A $4,800 annual tax bill adds $400 a month.

Homeowners insurance. Required by the lender, also collected via escrow. At $1,800 a year, that is $150 a month.

PMI. If your down payment is under 20%, private mortgage insurance protects the lender and typically costs 0.5% to 1% of the loan amount per year. On a $300,000 loan at 0.5%, that is $1,500 a year or $125 a month, until you reach 20% equity and can drop it.

HOA dues. Condos and some subdivisions charge monthly fees that never go away, often $100 to $400 or more.

Stack it up for our example with 20% down: $1,896.20 P&I + $400 tax + $150 insurance = $2,446.20 a month before any HOA. That gap between the formula answer and the real payment is where budgets get broken, so always calculate the full picture, not just P&I.

What happens if you pay extra every month?

Extra payments are the highest-return move in the mortgage world. Every extra dollar goes straight to principal, shrinking the balance that next month's interest is calculated on. The effect compounds in reverse.

Run our $300,000 loan at 6.5% again, but add $200 a month toward principal. The loan pays off in 277 months instead of 360, about 7 years early. Total interest falls from $382,632 to $279,185. That is $103,447 in interest saved for a $200 monthly habit.

One payment of an extra $200 is worth far more than it looks. In month one, your normal principal portion is $271.20; adding $200 nearly doubles the amount attacking the balance. That is why prepayment advice always says to start as early as possible: the math is kindest when the balance is largest.

My recommendation: if you can only do one smart thing with a mortgage, round your payment up by a fixed extra amount and automate it. Biweekly payment plans marketed by third parties often just split the payment in half and cost you fees; you can get the same effect free by paying a little extra principal each month yourself.

Should you choose a 15-year or 30-year loan?

Same $300,000 loan at 6.5%, but a 15-year term. Now n = 180 and (1+r)^180 = 2.645. The payment comes out to $2,613.32 a month, only about 38% more than the 30-year payment, not double as people often guess. Total interest over 15 years is $170,398 versus $382,632 for the 30-year: a savings of over $212,000.

So why does anyone take a 30-year loan? Flexibility. The 15-year loan locks you into the higher payment; if your income drops, that commitment can hurt. The 30-year loan keeps the required payment low, and nothing stops you from paying extra and finishing early anyway. You get most of the interest savings with an escape hatch built in.

Current context matters too. As of October 2026, Freddie Mac reports the average 30-year fixed rate at 7.40%, up from about 6.27% a year earlier. At higher rates the formula's interest total gets uglier, which makes the 15-year vs 30-year math and the extra-payment math even more worth doing before you sign.

What mistakes do people make when calculating by hand?

After watching people do this calculation for years, the same errors show up again and again. Here are the big ones.

Using the annual rate as the monthly rate. Plugging 0.065 straight into the formula instead of 0.065/12 gives a monthly payment of about $19,500 on our example loan. If your answer looks insane, this is usually why.

Using years instead of months for n. Putting n = 30 instead of 360 breaks the compounding completely. The exponent is the most powerful part of the formula; it has to be monthly.

Rounding r too early. Writing 0.0054 instead of 0.00541667 might look harmless, but the rate gets raised to the 360th power, so tiny rounding errors multiply. Keep at least six decimal places until the final answer.

Confusing APR with the rate. The APR includes some fees and can run slightly higher than the nominal rate used for the calculation. For a hand estimate, dividing the quoted rate by 12 is the correct approach; the lender's official Loan Estimate is the number that counts.

Forgetting escrow. People compute $1,896, budget $1,896, then get a $2,446 bill and wonder what happened. Always add tax, insurance, and PMI to the formula answer before deciding what you can afford.

How can you sanity-check your answer?

There is a quick rule of thumb hiding inside the formula. At 6.5% on a 30-year loan, the payment works out to about $6.32 for every $1,000 borrowed. Multiply by your loan size: $300,000 gives $300 × 6.32 = $1,896. That matches our worked example exactly.

This per-thousand trick is useful at the kitchen table. A $450,000 loan? About $2,844 a month P&I. A $200,000 loan? About $1,264. It only works for one rate and term at a time, but for quick comparisons between houses at the same rate, it is the fastest check there is.

And when you want the exact number without the button pushing, our free calculators do the whole thing, including taxes, insurance, PMI, and the extra-payment scenarios, in seconds.