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How Loan Payments Work
Whether you’re buying a home, financing a car, or taking out a personal loan, understanding how monthly payments are calculated helps you budget and compare offers. Most loans use an amortization schedule where each payment covers both principal and interest.
The Monthly Payment Formula
For a fixed-rate loan, the monthly payment is calculated using:
M = P × [r(1+r)^n] / [(1+r)^n - 1]
Where:
M= monthly paymentP= principal (loan amount)r= monthly interest rate (annual rate / 12)n= total number of payments (years × 12)
Step-by-Step Example
For a $250,000 mortgage at 6.5% interest over 30 years:
| Note | Result |
|---|---|
| principal = 250000 | 250,000 |
| annual rate = 6.5% | 6.50% |
| years = 30 | 30 |
| n = years × 12 | 360 |
| factor = (1 + annual rate / 12) ^ n | 6.99 |
| monthly payment = principal × (annual rate / 12 × factor) / (factor - 1) | 1,580.17 |
The monthly payment is 1,580.17. Displayed values are rounded to the app’s default two decimal places, while the calculation keeps full precision. That is why the monthly rate r (annual rate / 12, about 0.54%) is written inline: on its own line it would display as a rounded 0.01.
Over 30 years, you’ll pay:
| Note | Result |
|---|---|
| amount paid = monthly payment × n | 568,861.22 |
| amount paid - principal | 318,861.22 |
The right pane shows amount paid as 568,861.22 and the interest, amount paid - principal, as 318,861.22.
How Interest Rate Affects Payments
Small rate differences have a big impact over time. For a $300,000 loan over 30 years:
| Rate | Monthly Payment | Total Interest |
|---|---|---|
| 5.0% | $1,610 | $279,767 |
| 6.0% | $1,799 | $347,515 |
| 7.0% | $1,996 | $418,527 |
Each 1% increase adds roughly $200/month and $70,000 in total interest.
15-Year vs 30-Year Mortgage
For a $300,000 loan at 6.5%:
- 30-year:
$1,896/month, with$382,633in total interest - 15-year:
$2,613/month, with$170,398in total interest
The 15-year option saves $212,235 in interest but costs $717 more per month.
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Example
A $20,000 car loan at 5% for 5 years:
| Note | Result |
|---|---|
| principal = 20000 | 20,000 |
| monthly payment = 377.42 | 377.42 |
| n = 60 | 60 |
| amount paid = monthly payment × n | 22,645.20 |
| amount paid - principal | 2,645.20 |
Using the rounded monthly payment of 377.42, the totals are 22,645.20 paid and 2,645.20 in interest.
Frequently Asked Questions
How is a monthly loan payment calculated?
Monthly loan payments for fixed-rate loans use the amortization formula: M = P x [r(1+r)^n] / [(1+r)^n - 1], where P is the principal, r is the monthly interest rate, and n is the total number of payments. Each payment covers both principal and interest, with early payments being mostly interest.
Is a 15-year or 30-year mortgage better?
A 15-year mortgage has higher monthly payments but saves significantly on total interest. A 30-year mortgage offers lower monthly payments, giving more cash flow flexibility. For a $300,000 loan at 6.5%, the 15-year option saves over $200,000 in interest but costs about $700 more per month.
How does interest rate affect my total cost?
Even small rate differences compound dramatically over time. On a $300,000 30-year mortgage, each 1% increase in interest rate adds roughly $200 per month and about $70,000 in total interest paid over the life of the loan. Shopping for the best rate is one of the highest-impact financial decisions you can make.
Compare Loans in Notes Calculator
Notes Calculator’s variables and large number notation make mortgage comparisons fast. Put two terms side by side in one note:
| Note | Result |
|---|---|
| principal = 250k | 250,000 |
| annual rate = 6.5% | 6.50% |
| payment 30 years = principal × (annual rate / 12) / (1 - (1 + annual rate / 12) ^ -360) | 1,580.17 |
| payment 15 years = principal × (annual rate / 12) / (1 - (1 + annual rate / 12) ^ -180) | 2,177.77 |
| payment 15 years - payment 30 years | 597.60 |
The 30-year line matches the step-by-step example. This is the same fixed-rate amortization formula, rearranged so each term needs one line.
Type 250k instead of 250,000 for readability: Notes Calculator supports k (thousands), M (millions), and more. Use comments (//) to annotate each line, and headings (#) to separate different loan scenarios. Change principal or annual rate once and every calculation updates in real time.
Whether you are shopping for a home or already rent one out, our calculator for landlords and homebuyers reuses this payment formula: it sizes a down payment, adds tax and insurance for the real monthly cost of owning, and subtracts the payment from rent for a rental’s cash flow and gross yield.
Planning your financial future? See how your savings grow with our compound interest calculator, or calculate your profit margins if you are running a business.