Mortgage Payment Formula

Also known as: Loan Payment Formula, Amortization Formula, PMT Formula

M = P \frac{r(1+r)^n}{(1+r)^n - 1}

M = P × [r(1+r)^n] / [(1+r)^n - 1]

What It Calculates

Calculates the fixed monthly payment for a fully amortizing loan, where each payment covers both interest and principal.

Symbol	Name	Unit	Description
M	Monthly Payment	$	Fixed monthly mortgage payment
P	Principal	$	Loan amount (home price minus down payment)
r	Monthly Rate	decimal	Annual rate divided by 12
n	Total Payments	—	Loan term in months (years × 12)

1r = 0.065/12 = 0.005417

2n = 30 × 12 = 360

3(1.005417)^360 = 6.9916

4M = 300000 × (0.005417 × 6.9916) / (6.9916 - 1)

5M = $1,896.20

Result: $1,896.20

r is the MONTHLY rate, not annual — divide by 12

n is total months, not years

This doesn't include taxes, insurance, or PMI

A = P(1 + r/n)^(nt)

PV = FV / (1 + r/n)^(nt)

DTI = (Total Monthly Debt / Gross Monthly Income) × 100

#mortgage#loan#amortization#home buying