Mortgage Payment Formula: Step-by-Step with Examples
The mortgage payment formula calculates your exact monthly payment based on loan amount, interest rate, and term. Understanding it helps you compare loan offers, negotiate rates, and plan your budget accurately. This guide walks through every step with real numbers.
The Mortgage Payment Formula
M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]
Step-by-Step Calculation
Example: $320,000 loan at 7% annual interest for 30 years.
Convert annual rate to monthly
r = Annual Rate ÷ 12
7% ÷ 12 = 0.5833% per month (0.005833)
Calculate total number of payments
n = Years × 12
30 years × 12 = 360 monthly payments
Apply the mortgage formula
M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]
$320,000 × [0.005833 × (1.005833)³⁶⁰] / [(1.005833)³⁶⁰ − 1] = $2,129/mo
Result for $320,000 at 7% for 30 years:
$2,129 / month
Total interest paid: $446,440 over 30 years
Try It: Calculate Your Mortgage Payment
Monthly Payment
$2,128.97
Total Interest
$446,428
Total Cost
$766,428
First 12 Months Amortization Schedule
| Month | Payment | Principal | Interest | Balance |
|---|---|---|---|---|
| 1 | $2,128.97 | $262.30 | $1,866.67 | $319,738 |
| 2 | $2,128.97 | $263.83 | $1,865.14 | $319,474 |
| 3 | $2,128.97 | $265.37 | $1,863.60 | $319,208 |
| 4 | $2,128.97 | $266.92 | $1,862.05 | $318,942 |
| 5 | $2,128.97 | $268.48 | $1,860.49 | $318,673 |
| 6 | $2,128.97 | $270.04 | $1,858.93 | $318,403 |
| 7 | $2,128.97 | $271.62 | $1,857.35 | $318,131 |
| 8 | $2,128.97 | $273.20 | $1,855.77 | $317,858 |
| 9 | $2,128.97 | $274.79 | $1,854.17 | $317,583 |
| 10 | $2,128.97 | $276.40 | $1,852.57 | $317,307 |
| 11 | $2,128.97 | $278.01 | $1,850.96 | $317,029 |
| 12 | $2,128.97 | $279.63 | $1,849.34 | $316,749 |
Notice: early payments are mostly interest. Principal paydown accelerates over time.
How Rate Changes Affect Your Payment ($300,000 Loan, 30 Years)
| Rate | Monthly | Total Interest | vs 7% |
|---|---|---|---|
| 5% | $1,610.46 | $279,767 | $0.00/mo |
| 5.5% | $1,703.37 | $313,212 | $0.00/mo |
| 6% | $1,798.65 | $347,515 | $0.00/mo |
| 6.5% | $1,896.20 | $382,633 | $0.00/mo |
| 7% ★ | $1,995.91 | $418,527 | — |
| 7.5% | $2,097.64 | $455,152 | +$101.74/mo |
| 8% | $2,201.29 | $492,466 | +$205.39/mo |
| 8.5% | $2,306.74 | $530,427 | +$310.83/mo |
A 1% rate difference on a $300k loan = ~$180/month or $65,000 over 30 years.
Key Insights from the Mortgage Formula
Early payments are mostly interest
In month 1 of a $320k loan at 7%, only $262 goes to principal — $1,867 goes to interest. By year 20, the split reverses. This is why extra principal payments early have massive impact.
Rate matters more than term
Dropping from 7% to 6% on a $300k loan saves $180/month and $65,000 total. Refinancing when rates drop 1%+ is almost always worth it if you plan to stay 3+ years.
Extra payments are powerful
Adding $200/month to a $320k, 30-year, 7% mortgage cuts the term by 5 years and saves $87,000 in interest. Even one extra payment per year saves 4 years.
Related Mortgage & Finance Resources
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Open Mortgage CalculatorQuick Formula
M = P × r(1+r)ⁿ / (1+r)ⁿ−1
r = annual rate ÷ 12
n = years × 12