How mortgage payments are calculated

A fixed-rate mortgage is designed so that one identical payment, made every month for the whole term, pays the interest due and leaves the balance at exactly zero after the last payment. This guide shows how that payment is found, why the early years are mostly interest, and which levers actually change what you pay.

Interest is charged on what you still owe

Mortgage interest is simple interest charged monthly on the outstanding balance. With an annual rate of 6.5%, the monthly rate is 6.5% ÷ 12 = 0.5417%. On a $320,000 balance, the first month’s interest is:

Whatever you pay above that interest reduces the balance. Next month interest is charged on the new, slightly smaller balance — so interest falls a little every month and, with a fixed payment, the principal share grows.

Finding the payment that clears the loan

We need a payment M that, after n months, brings the balance to zero. Track the balance month by month with a monthly rate r: after one payment it is P(1 + r) − M; after two, P(1 + r)² − M(1 + r) − M; and after n payments:

The second term is a geometric series: each payment earns (or rather, stops) interest for a different number of months. Setting the balance to zero and solving for M gives the standard formula:

M

monthly principal and interest payment

P

amount borrowed

r

monthly rate as a decimal (annual rate ÷ 12)

n

number of payments (years × 12)

When the rate is zero the formula divides by zero, but the limit is what you would expect: M = P ÷ n.

A worked example

Take a $320,000 loan at 6.5% for 30 years.

1. r = 0.065 ÷ 12 = 0.00541667
2. n = 30 × 12 = 360
3. (1 + r)ⁿ = 1.00541667³⁶⁰ ≈ 6.99179
4. M = 320,000 × 0.00541667 × 6.99179 ÷ 5.99179 ≈ $2,022.62

Here is how the first three payments split, with each month’s interest rounded to the cent:

In month one, 86% of the payment is interest. The split crosses 50/50 only around year 19, and in the final year almost all of each payment is principal. Over the full term, interest adds up to about $408,100.

What actually changes the payment

The interest rate

On the same $320,000 over 30 years, the payment is $1,918.56 at 6%, $2,022.62 at 6.5% and $2,128.97 at 7%. Each half point moves the payment by roughly $105 a month and total interest by roughly $38,000.

The term

Shortening the term raises the payment but cuts interest sharply, because the balance is repaid faster. At 6.5%, a 15-year loan costs $2,787.54 a month and about $181,800 in interest — less than half the 30-year total.

Extra principal

An extra payment goes entirely to principal, and every dollar of principal removed stops generating interest for the rest of the loan. Paying an extra $200 a month on the example loan ends it after 281 payments instead of 360 and saves about $105,000 in interest.

Beyond principal and interest

Most US lenders also collect property tax and homeowners insurance each month through an escrow account, and add private mortgage insurance when the down payment is under 20%. These are not part of the amortization formula; they are added on top and can change from year to year. The mortgage calculator includes them so you see the full monthly cost.