The Mortgage Payment Formula, Plainly Explained
Most mortgages are fixed-rate loans: you pay the same amount every month until the loan is gone. That monthly amount comes from the standard amortization formula:
M = P [r(1+r)n] / [(1+r)n - 1]
Here is what each part means. P is the principal, the amount you actually borrow. r is the monthly interest rate, which is your annual rate divided by 12 (so 6.5% becomes 0.065 / 12 = 0.005417). n is the total number of monthly payments: 360 for a 30-year loan, 180 for a 15-year loan. The result, M, is your fixed monthly payment covering principal and interest.
The formula looks intimidating, but the idea is simple. Early payments are mostly interest; over time the interest portion shrinks and the principal portion grows, while the total payment stays the same. The formula just packs that whole schedule into one number.
A Worked Example
Say you borrow $400,000 at 6.5% for 30 years. First convert the inputs: P = 400,000, r = 0.005417, n = 360.
Compute (1 + r)^n: 1.005417^360 is about 6.99. Then the numerator is r times that: 0.005417 x 6.99 = 0.03788. The denominator is 6.99 - 1 = 5.99. So M = 400,000 x (0.03788 / 5.99) = 400,000 x 0.006322, which comes out to roughly $2,529 per month in principal and interest.
Over 30 years you would pay about $910,000 total, meaning roughly $510,000 of it is interest alone. That is the power of compounding working against you, and it is why a lower rate or shorter term saves so much.
PITI: Your Real Monthly Housing Cost
The formula above covers principal and interest only. Your actual monthly check usually includes two more items, together known as PITI: Principal, Interest, Taxes, and Insurance.
Property taxes are set by your local government and collected monthly through escrow, then paid to the county on your behalf. Homeowners insurance is required by the lender and also collected through escrow. On top of that, if your down payment is under 20%, expect PMI (private mortgage insurance), another monthly line item that protects the lender, not you. HOA dues are a separate payment entirely.
A $2,529 principal-and-interest payment can easily become $3,300 or more once taxes, insurance, and PMI are added. When budgeting for a home, always calculate PITI, not just the loan payment.
What Changes Your Payment
Three levers move the number. Rate: on that same $400,000 30-year loan, dropping the rate from 6.5% to 6.0% saves about $130 a month and roughly $46,000 in lifetime interest. Small rate differences compound into huge sums. Term: switching from 30 years to 15 at the same rate pushes the monthly payment up by about 50% but cuts total interest by more than two-thirds. Down payment: more money down means a smaller P, which lowers both the payment and the interest, and 20% down also eliminates PMI.
Frequently Asked Questions
What is the formula to calculate a mortgage payment?
M = P [r(1+r)n] / [(1+r)n - 1], where P is the loan amount, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. This gives the fixed monthly principal and interest payment.
What does PITI stand for?
PITI stands for Principal, Interest, Taxes, and Insurance. It is the full monthly housing cost: the loan payment plus property taxes and homeowners insurance, which are usually collected through escrow.
How much does a 1% rate change affect my mortgage payment?
On a $400,000 30-year loan, a 1% rate increase (from 6.5% to 7.5%) raises the monthly principal and interest payment by roughly $260 to $270. Over the life of the loan that is about $95,000 in extra interest.
Is a 15-year mortgage always better than a 30-year?
Not always. A 15-year loan has a higher monthly payment but far less total interest. A 30-year loan costs more in interest but keeps payments lower, which can matter for cash flow. The best choice depends on your budget and goals.