Sarah has 12 years of experience specializing in personal debt management and loan structuring across mortgage and consumer finance sectors.
The **Loan Amortization Calculator** helps you understand the full life cycle of your loan, including interest paid vs. principal paid over time. This flexible calculator allows you to solve for the **Principal Loan Amount (P)**, **Periodic Payment (PMT)**, **Annual Interest Rate (R)**, or **Loan Term (N)**. **Input any three of the four core variables** to find the missing one.
Loan Amortization Calculator
Loan Amortization Formulas
Amortization refers to the process of paying off debt over time in regular installments. The core formula links the principal, rate, term, and payment amount:
Where $i = \frac{R}{1200}$ (Monthly Interest Rate, decimal) and $n = N \times 12$ (Total Number of Monthly Payments).
Formula Source: Investopedia: Loan Amortization Schedule
Variables Explained
Understanding these variables is crucial for managing any amortized loan:
- Principal Loan Amount (P, F): The total amount of money borrowed ($).
- Periodic Payment (PMT, P): The fixed monthly amount paid to the lender ($).
- Annual Interest Rate (R, V): The yearly nominal interest rate (%). This assumes monthly compounding.
- Loan Term (N, Q): The total duration of the loan (Years).
Related Calculators
Optimize your borrowing and savings strategies with these related financial tools:
- Total Loan Interest Calculator
- Loan Payoff Date Calculator
- Extra Payment Impact Calculator
- Present Value of Annuity Calculator
What is Loan Amortization?
**Loan amortization** is the process of gradually paying off a debt over a fixed period through regular installments. Each payment covers both the interest accrued since the last payment and a portion of the principal balance. The key feature of an amortized loan is that the payment amount remains constant throughout the loan term, while the interest-to-principal ratio within that payment changes.
In the early stages, the majority of your payment goes toward interest, resulting in slow principal reduction. As the principal shrinks, the interest portion of the payment decreases, and more of the fixed payment is applied toward the principal, accelerating the payoff toward the end of the term.
How to Calculate Loan Payment (Example)
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Identify Components:
We want to find the Payment ($PMT$). Principal ($\mathbf{P}$) is $\mathbf{\$100,000}$. Annual Rate ($\mathbf{R}$) is $\mathbf{6\%}$. Loan Term ($\mathbf{N}$) is $\mathbf{10}$ years.
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Convert to Monthly Terms (i and n):
Monthly Rate ($\mathbf{i}$) is $\frac{6\%}{1200} = \mathbf{0.005}$. Total Payments ($\mathbf{n}$) is $10 \times 12 = \mathbf{120}$ payments.
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Apply the Formula:
Using the payment formula: $$ PMT = 100000 \times \frac{0.005(1+0.005)^{120}}{(1+0.005)^{120} – 1} $$
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Determine the Monthly Payment:
The calculation yields a monthly payment ($\mathbf{PMT}$) of approximately $\mathbf{\$1,109.52}$.
Frequently Asked Questions (FAQ)
A: Interest is always calculated based on the *remaining* principal balance. Since the principal is highest at the start, the interest portion of the fixed payment is also highest, leaving less to reduce the principal.
A: Making extra payments directly reduces the principal balance. This lowers the base on which future interest is calculated, resulting in significant savings on total interest paid and a shorter loan term.
A: Yes, this calculator uses the standard formula for fixed-rate, fully amortizing loans, which is the basis for most traditional mortgages, car loans, and personal loans.
A: The core formula does not directly solve for interest-only payments, as they involve no principal reduction. However, the interest component of any payment (Principal * Monthly Rate) can be calculated easily.