How to Calculate Monthly Mortgage Payments: The Complete Amortization Formula
The exact mathematical breakdown of fixed-rate mortgage payments, principal vs. interest amortization, PITI escrow, and spreadsheet formulas.
- What is the formula to calculate a monthly mortgage payment?
- What does PITI stand for and how is it calculated?
- How does an amortization schedule change over 30 years?
- How much interest do extra mortgage principal payments save?
1. The Standard Mortgage Amortization Formula
To calculate the fixed monthly principal and interest payment on a mortgage, lenders use the standard annuity amortization formula.
In this formula, M is your monthly payment, P is the principal loan amount, r is your monthly interest rate (annual interest rate divided by 12), and n is the total number of monthly payments (loan term in years multiplied by 12).
2. Worked Example: $400,000 Loan at 6.5%
Consider a homebuyer taking out a $400,000 loan on a 30-year fixed term at 6.50% annual interest.
Step 1: Convert the annual rate to a monthly decimal: 0.065 / 12 = 0.0054167. Step 2: Calculate total monthly periods: 30 * 12 = 360 months. Step 3: Solve the annuity fraction: [0.0054167 * (1.0054167)^360] / [(1.0054167)^360 - 1] = 0.0063207. Step 4: Multiply by principal: $400,000 * 0.0063207 = $2,528.27 monthly payment.
| Year Milestone | Monthly Payment | Principal Paid | Interest Paid | Remaining Loan Balance |
|---|---|---|---|---|
| Month 1 | $2,528.27 | $361.60 | $2,166.67 | $399,638.40 |
| Year 5 (Month 60) | $2,528.27 | $473.19 | $2,055.08 | $378,941.52 |
| Year 15 (Month 180) | $2,528.27 | $899.41 | $1,628.86 | $299,842.18 |
| Year 25 (Month 300) | $2,528.27 | $1,709.61 | $818.66 | $150,912.44 |
| Final (Month 360) | $2,528.27 | $2,514.65 | $13.62 | $0.00 |
3. Understanding PITI (Taxes and Insurance Escrow)
Your actual monthly check to the mortgage servicer is almost always higher than just principal and interest. Lenders collect property taxes and homeowners insurance in an escrow account.
PITI stands for Principal, Interest, Taxes, and Insurance. If your annual property taxes are $6,000 ($500/month) and homeowners insurance is $1,800 ($150/month), your total monthly housing obligation is $2,528.27 + $500.00 + $150.00 = $3,178.27.
4. How Extra Principal Payments Slash Total Interest
Because monthly interest is calculated against your remaining balance, every extra dollar paid directly toward principal permanently reduces interest in all future months.
Paying an extra $150 per month toward principal on this $400,000 loan cuts your payoff timeline from 30 years down to 25.5 years, saving over $78,000 in lifetime interest.
5. Excel and Google Sheets PMT Formula
In Microsoft Excel or Google Sheets, calculate your monthly payment with the built-in PMT function:
=PMT(6.5% / 12, 30 * 12, -400000)Enter annual rate divided by 12, total months, and negative loan amount to return a positive payment amount.
Frequently Asked Questions
Direct answers to the most common questions people ask online about this topic.
How does loan amortization work?
In the early years of a mortgage, the majority of your monthly payment goes toward interest. As your balance drops, the interest portion shrinks and the principal portion expands until the loan is fully retired.
What is Private Mortgage Insurance (PMI)?
If your down payment is less than 20% on a conventional loan, lenders require PMI to protect against default. PMI typically costs 0.5% to 1.5% of the original loan amount annually until you reach 20% equity.
What is the difference between a 15-year and a 30-year mortgage?
A 15-year mortgage has higher monthly payments but lower interest rates. Over the life of the loan, a 15-year mortgage saves tens of thousands of dollars in total interest compared to a 30-year loan.