Understanding Mortgages: The Basics
A mortgage is a loan specifically designed to purchase real estate, where the property itself serves as collateral. For most people, it's the largest financial commitment they'll ever make -- and understanding how mortgages work can save you tens of thousands of dollars over the life of the loan.
Whether you're a first-time homebuyer or looking to refinance, this comprehensive guide will help you understand every aspect of mortgage calculations, from the basic payment formula to advanced strategies for saving money.
Use our free mortgage calculator to estimate your monthly payments. Open Mortgage Calculator →
The Mortgage Payment Formula
The standard formula for calculating a fixed-rate mortgage monthly payment is:
M = P × [r(1 + r)n] / [(1 + r)n − 1]
Where:
- M = Monthly payment
- P = Principal (loan amount)
- r = Monthly interest rate (annual rate ÷ 12)
- n = Total number of payments (years × 12)
Step-by-Step Example
Let's calculate the monthly payment for a $350,000 home with 20% down at 6.5% interest for 30 years:
- Down payment: $350,000 × 0.20 = $70,000
- Loan amount (P): $350,000 − $70,000 = $280,000
- Monthly rate (r): 6.5% ÷ 12 = 0.005417
- Total payments (n): 30 × 12 = 360
M = 280,000 × [0.005417 × (1.005417)360] / [(1.005417)360 − 1]
M = 280,000 × [0.005417 × 6.9913] / [6.9913 − 1]
M = 280,000 × 0.03787 / 5.9913
M = $1,770.09/month (principal and interest only)
Over 30 years, you'd pay a total of $637,232 -- meaning $357,232 goes to interest alone. That's more than the original loan amount!
What's Included in Your Monthly Payment (PITI)
Your total monthly housing payment includes more than just principal and interest. The full PITI breakdown:
| Component | Description | Example (on $350K home) |
|---|---|---|
| Principal | Pays down the loan balance | Varies (starts ~$250) |
| Interest | Cost of borrowing | Varies (starts ~$1,520) |
| Taxes | Property tax (escrowed) | ~$365/month (1.25%) |
| Insurance | Homeowner's insurance | ~$150/month |
| PMI (if applicable) | Private mortgage insurance | ~$140/month (if <20% down) |
| HOA (if applicable) | Homeowner association dues | $0-$500+/month |
Total estimated payment: $1,770 (P&I) + $365 (taxes) + $150 (insurance) = $2,285/month
Fixed-Rate vs. Adjustable-Rate Mortgages
Fixed-Rate Mortgage (FRM)
The most popular choice -- your interest rate stays the same for the entire loan term.
- Pros: Predictable payments, protection from rate increases, easier to budget
- Cons: Higher initial rate than ARMs, you miss out if rates drop (unless you refinance)
- Best for: People who plan to stay in the home long-term, risk-averse borrowers, when rates are historically low
Adjustable-Rate Mortgage (ARM)
Your rate is fixed for an initial period, then adjusts periodically. Common types include 5/1, 7/1, and 10/1 ARMs (the first number is the fixed period in years; the second is how often it adjusts after).
- Pros: Lower initial rate (typically 0.5-1% less than fixed), potential savings if you sell or refinance before the adjustment period
- Cons: Payment uncertainty after fixed period, rates can increase significantly, more complex to understand
- Best for: People who plan to move within 5-7 years, borrowers who expect rates to decrease, those who need lower initial payments
Side-by-Side Comparison
On a $280,000 loan:
| Feature | 30-Year Fixed (6.5%) | 5/1 ARM (5.5% → adjusts) |
|---|---|---|
| Initial monthly payment | $1,770 | $1,590 |
| Monthly savings (first 5 years) | -- | $180/month ($10,800 total) |
| Payment if rate rises to 8.5% | $1,770 (unchanged) | ~$2,100 |
| Payment certainty | 100% | First 5 years only |
How Amortization Works
Amortization is how your loan is gradually paid off through scheduled payments. The key insight is that early payments are mostly interest, while later payments are mostly principal.
Here's what amortization looks like for a $280,000 loan at 6.5% over 30 years:
| Payment | Monthly Payment | Principal | Interest | Remaining Balance |
|---|---|---|---|---|
| Month 1 | $1,770 | $253 | $1,517 | $279,747 |
| Month 60 (Year 5) | $1,770 | $343 | $1,427 | $262,506 |
| Month 120 (Year 10) | $1,770 | $470 | $1,300 | $239,076 |
| Month 180 (Year 15) | $1,770 | $644 | $1,126 | $206,780 |
| Month 240 (Year 20) | $1,770 | $882 | $888 | $162,517 |
| Month 300 (Year 25) | $1,770 | $1,207 | $563 | $102,521 |
| Month 360 (Year 30) | $1,770 | $1,761 | $9 | $0 |
Notice: In month 1, only $253 (14%) goes to principal. By month 240 (year 20), the split is roughly 50/50. By the final years, almost your entire payment goes to principal.
Down Payment: How Much Do You Need?
The down payment is the upfront cash you put toward the home purchase. Here's how different down payment amounts affect a $350,000 home at 6.5% for 30 years:
| Down Payment | Amount | Loan Amount | Monthly P&I | PMI | Total Monthly |
|---|---|---|---|---|---|
| 3% | $10,500 | $339,500 | $2,146 | ~$170 | $2,316 |
| 5% | $17,500 | $332,500 | $2,102 | ~$166 | $2,268 |
| 10% | $35,000 | $315,000 | $1,991 | ~$131 | $2,122 |
| 20% | $70,000 | $280,000 | $1,770 | $0 | $1,770 |
| 25% | $87,500 | $262,500 | $1,659 | $0 | $1,659 |
Going from 3% to 20% down saves $546/month ($6,552/year). Over 30 years, that's over $196,000 in savings including eliminated PMI and reduced interest.
First-Time Buyer Programs
- FHA Loans: 3.5% down with 580+ credit score; require upfront and annual mortgage insurance
- VA Loans: 0% down for veterans and active military; no PMI required
- USDA Loans: 0% down for rural/suburban properties; income limits apply
- Conventional 97: 3% down; requires PMI until 20% equity
- State/local programs: Down payment assistance, grants, and subsidized rates vary by location
Understanding PMI (Private Mortgage Insurance)
PMI protects the lender (not you) if you default on the loan. It's required when your down payment is less than 20%. PMI costs typically range from 0.5% to 1.5% of the original loan amount per year.
How to Get Rid of PMI
- Automatic termination: By law, PMI must be canceled when your loan-to-value (LTV) ratio reaches 78% based on the original schedule
- Request removal at 80% LTV: You can request removal once you reach 20% equity (through payments or home value increase)
- Refinance: If your home has appreciated significantly, refinancing may eliminate PMI
- Reappraisal: Some lenders allow a new appraisal to demonstrate increased equity
The DTI Ratio: How Lenders Determine Affordability
Your Debt-to-Income (DTI) ratio is one of the most important factors lenders consider. It measures what percentage of your gross monthly income goes toward debt payments.
Front-end DTI = Monthly Housing Costs / Gross Monthly Income × 100
Back-end DTI = All Monthly Debt Payments / Gross Monthly Income × 100
Example DTI Calculation
Gross monthly income: $8,000
- Proposed mortgage (PITI): $2,000
- Car payment: $400
- Student loans: $300
- Credit card minimums: $100
Front-end DTI: $2,000 / $8,000 = 25% ✅ (under 28%)
Back-end DTI: $2,800 / $8,000 = 35% ✅ (under 36%)
DTI Guidelines by Loan Type
| Loan Type | Max Front-End DTI | Max Back-End DTI |
|---|---|---|
| Conventional | 28% | 36-45% |
| FHA | 31% | 43-50% |
| VA | No strict limit | 41% |
| USDA | 29% | 41% |
15-Year vs. 30-Year Mortgage: Which Is Better?
This is one of the most impactful financial decisions you'll make. Let's compare on a $280,000 loan:
| Feature | 15-Year (5.75%) | 30-Year (6.5%) |
|---|---|---|
| Monthly payment (P&I) | $2,326 | $1,770 |
| Total paid over loan | $418,680 | $637,232 |
| Total interest paid | $138,680 | $357,232 |
| Interest savings | $218,552 less | -- |
| Monthly payment difference | -- | $556 less/month |
The 15-year mortgage saves over $218,000 in interest but requires $556 more per month. Choose based on your financial situation and goals.
Strategies to Save Money on Your Mortgage
- Make extra principal payments. Even $100/month extra on a $280,000 loan at 6.5% saves over $62,000 in interest and pays off the loan 5 years early.
- Bi-weekly payments. Paying half your monthly payment every two weeks results in 26 half-payments (13 full payments) per year instead of 12, shaving about 4 years off a 30-year mortgage.
- Refinance when rates drop. A general rule: refinancing is worth it if you can reduce your rate by at least 0.75-1% and you'll stay in the home long enough to recoup closing costs.
- Avoid the maximum. Just because you qualify for a $400,000 mortgage doesn't mean you should take one. Aim for housing costs below 25% of take-home pay.
- Shop multiple lenders. Rates can vary by 0.5% or more between lenders. On a $280,000 loan, that's thousands over the life of the loan.
- Buy points. Paying 1% of the loan amount upfront (one "point") typically reduces your rate by 0.25%. This saves money if you keep the loan long enough.
- Improve your credit score before applying. A 740+ score qualifies for the best rates. Even a 0.5% rate difference saves $30,000+ over 30 years on a $280,000 loan.
- Consider a shorter term. If you can afford higher payments, a 15 or 20-year term saves massively on interest.
How Much House Can You Afford?
Use this quick framework to estimate your maximum home price:
- Calculate 28% of gross monthly income: $8,000 × 0.28 = $2,240 max housing payment
- Subtract estimated taxes and insurance: $2,240 − $500 = $1,740 for P&I
- Use a mortgage calculator to find the loan amount: At 6.5% for 30 years, $1,740/month ≈ $275,000 loan
- Add your down payment: $275,000 + $55,000 (20% down) = $344,000 home price
This is a maximum -- many financial advisors recommend keeping housing costs closer to 20-25% of take-home pay for a comfortable lifestyle.
Explore More Financial Tools
- Mortgage Calculator -- Calculate your exact monthly payment
- Loan Calculator -- Calculate any loan payment
- Savings Goal Calculator -- Save for your down payment
- Compound Interest Guide -- Understand how your savings grow
- Percentage Calculator Guide -- Master percentage calculations
Use our free mortgage calculator to plan your home purchase. Calculate Mortgage Payment →
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Frequently Asked Questions
How much mortgage can I afford?
A common guideline is the 28/36 rule: spend no more than 28% of gross monthly income on housing costs and no more than 36% on total debt. For a $6,000/month gross income, that means a maximum mortgage payment of about $1,680/month, which at 6.5% interest for 30 years supports roughly a $265,000 loan.
What is the mortgage payment formula?
The monthly payment formula is M = P[r(1+r)^n]/[(1+r)^n - 1], where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of payments. For a $300,000 loan at 6.5% for 30 years: r = 0.005417, n = 360, M = $1,896.20/month.
What is the difference between fixed and adjustable rate mortgages?
A fixed-rate mortgage keeps the same interest rate for the entire loan term (15 or 30 years), providing predictable payments. An adjustable-rate mortgage (ARM) has a lower initial rate for a set period (e.g., 5 years) then adjusts periodically based on market rates, which can increase or decrease your payment.
How much should I put down on a house?
The traditional recommendation is 20% down to avoid PMI. However, many programs allow less: FHA loans require as little as 3.5%, VA loans require 0%, and conventional loans can start at 3-5%. A larger down payment reduces monthly payments and total interest paid.
What is PMI and how do I avoid it?
Private Mortgage Insurance (PMI) is required when your down payment is less than 20% of the home price. It typically costs 0.5-1.5% of the loan amount per year. You can avoid PMI by putting 20% down, using a VA loan, or requesting PMI removal once you reach 20% equity.
What is a good DTI ratio for a mortgage?
Most lenders prefer a front-end DTI (housing costs only) below 28% and a back-end DTI (all debts) below 36%. FHA loans may accept up to 43%, and some conventional programs allow up to 50% with strong compensating factors like high credit scores or large cash reserves.
Should I get a 15-year or 30-year mortgage?
A 15-year mortgage has higher monthly payments but saves significantly on interest -- often 50-60% less total interest. A 30-year mortgage has lower payments, giving more financial flexibility. Choose 15 years if you can comfortably afford the higher payment; otherwise, a 30-year with extra principal payments is a good compromise.
How does amortization work?
Amortization is the process of paying off a loan through scheduled payments of principal and interest. In the early years, most of your payment goes to interest. Over time, the balance shifts toward principal. On a 30-year $300,000 loan at 6.5%, only $271 of your first $1,896 payment goes to principal.
What credit score do I need for a mortgage?
Minimum credit scores vary by loan type: Conventional loans typically require 620+, FHA loans require 580+ (or 500 with 10% down), VA loans have no official minimum but lenders often require 620+. Higher scores (740+) qualify for the best interest rates, potentially saving tens of thousands over the loan term.
Are mortgage rates tax deductible?
Yes, mortgage interest is tax-deductible on the first $750,000 of mortgage debt ($375,000 if married filing separately) for loans taken after December 15, 2017. You must itemize deductions to claim this benefit. Property taxes are also deductible up to $10,000 combined with state/local taxes.