David is a Chartered Financial Analyst and former mortgage banker with 15 years of experience in loan origination and financial modeling.
This 4-in-1 Loan Amortization calculator helps you solve any part of your loan equation. Enter any three values—Loan Amount, Annual Rate, Term, or Monthly Payment—and we will solve for the fourth.
Loan Amortization Calculator
Loan Amortization Formulas
i = R / 12 / 100 (Monthly Rate)
n = T * 12 (Number of Months)
Solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Solve for Loan Amount (P):
P = M * [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]
Solve for Term (n):
n = log( M / (M – P*i) ) / log(1 + i)
Solve for Rate (i):
(No direct formula; solved iteratively)
Formula Variables
- (P) Loan Amount: The total principal amount borrowed from the lender.
- (R) Annual Rate: The nominal annual interest rate for the loan (e.g., 6.5%).
- (T) Loan Term: The total number of years you have to repay the loan (e.g., 30).
- (M) Monthly Payment: The fixed monthly payment (principal + interest) required to repay the loan in full over the term.
Related Calculators
- Mortgage Payment Calculator
- Loan Affordability Calculator
- Debt to Income (DTI) Calculator
- Simple Interest Calculator
What is Loan Amortization?
Loan amortization is the process of spreading out a loan into a series of fixed, equal payments over a set period of time. Each payment consists of two parts: **principal** and **interest**. At the beginning of the loan, the majority of your payment goes toward interest. As time goes on, a larger and larger portion of your payment goes toward paying down the principal (the amount you borrowed).
An **amortization schedule** is a table that details exactly how much of each payment goes to interest and how much to principal, and what your remaining loan balance is after every payment. This schedule shows you the “inside story” of your loan and provides a clear path to becoming debt-free.
Understanding amortization is crucial for any borrower. It helps you see the true cost of your loan (the total interest paid) and how factors like the interest rate and loan term dramatically affect that cost. For example, a 30-year mortgage will have much lower monthly payments than a 15-year mortgage, but you will pay significantly more in total interest over the life of the loan.
How to Calculate Amortization (Example)
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Identify Loan Variables
You are getting a mortgage with the following terms:
• Loan Amount (P): $300,000
• Annual Rate (R): 7%
• Loan Term (T): 30 years -
Convert to Monthly Terms (i, n)
The formula uses monthly values:
• Monthly Rate (i): 7% / 12 / 100 = 0.005833
• Number of Months (n): 30 years * 12 = 360 -
Choose the Payment Formula
Use the standard formula to solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ] -
Calculate the Monthly Payment
Plug in the monthly values:
• Numerator: 0.005833 * (1 + 0.005833)^360 = 0.04747
• Denominator: (1 + 0.005833)^360 – 1 = 7.1077
M = $300,000 * [ 0.04747 / 7.1077 ]
M = $300,000 * 0.006679 = $2,003.70
Your monthly payment is $2,003.70.
Frequently Asked Questions (FAQ)
How can I use this to find my loan amount?
Enter the Monthly Payment (M) you can afford (e.g., $2,000), the current Annual Rate (R) (e.g., 6.5%), and the Loan Term (T) (e.g., 30). The calculator will solve for the Loan Amount (P) you can borrow, which is essential for home shopping.
What does “fully amortized” mean?
A fully amortized loan is one where the loan will be completely paid off (the balance will be $0) at the end of the term if you make every scheduled payment. Most standard mortgages and auto loans are fully amortized. An “interest-only” loan is *not* amortized, as your payments only cover interest and the principal never decreases.
How can I use this to find the interest rate?
This is a powerful feature for checking loan offers. Enter the Loan Amount (P), the Loan Term (T), and the quoted Monthly Payment (M). The calculator will solve for the Annual Rate (R). This helps you discover the *true* interest rate and see if it matches what you were quoted, or uncover hidden fees.
How can I use this to see how fast I can pay off a loan?
Enter your Loan Amount (P), the Annual Rate (R), and the (higher) Monthly Payment (M) you plan to make. The calculator will solve for the Loan Term (T). This will show you how many years you can shave off your loan by paying extra each month.