David Chen is a CPA and financial consultant with 18 years of experience in debt restructuring, loan modeling, and small business finance.
The **Loan Amortization Period Calculator** uses the principal loan amount, the periodic interest rate, and the fixed payment amount to determine the total **Number of Periods ($N$)** required to fully pay off the debt. This versatile four-variable calculator solves for any missing input: **Loan Principal ($P$)**, **Periodic Payment ($PMT$)**, **Interest Rate ($R$)**, or the **Number of Periods ($N$)**. **Input any three of the four core variables** to find the missing one.
Loan Amortization Period Calculator
Loan Amortization Formulas
The core relationship is based on the Present Value of an Annuity formula, which links the loan principal ($P$) to the stream of equal payments ($PMT$) discounted at the periodic rate ($r$) over $N$ periods.
Note: $r$ is the decimal rate per period ($R_{percent}/100$).
Formula Source: Investopedia: Present Value of Annuity Formula
Variables Explained
These are the four core components of an amortizing loan calculation:
- Loan Principal (P): The initial amount of money borrowed ($).
- Periodic Payment (PMT): The constant amount paid each period (e.g., monthly) ($).
- Interest Rate (R): The interest rate applied *per payment period* (%).
- Number of Periods (N): The total number of periods (e.g., months) required to repay the loan.
Related Calculators
Use these related loan tools to manage your debt:
- Loan Payment Calculator
- Amortization Schedule Calculator
- Extra Payment Impact Calculator
- Simple vs. Compound Interest Calculator
What is Loan Amortization Period?
The **Amortization Period** refers to the total length of time, typically measured in months or years, that it takes to pay off a loan fully by making fixed, scheduled payments. In an amortizing loan, each payment covers both the interest accrued since the last payment and a portion of the principal balance. The period is complete when the entire principal, plus all accumulated interest, has been repaid.
For financial planning, knowing the exact number of periods (N) allows borrowers to budget for the future and determine the true cost of credit. If the calculated period is too long, the borrower may need to increase the periodic payment (PMT) or seek a lower interest rate (R).
How to Calculate Amortization Period (Example)
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Identify Components:
A loan has a $\mathbf{P}$ of $\mathbf{\$20,000}$, $\mathbf{PMT}$ of $\mathbf{\$500}$, and a monthly rate ($\mathbf{r}$) of $\mathbf{0.5\%}$ ($\mathbf{R}$ of $\mathbf{0.005}$ decimal).
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Determine the Ratio:
Calculate $\frac{P \cdot r}{PMT} = \frac{\$20,000 \times 0.005}{\$500} = \mathbf{0.2}$
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Apply the Formula:
$$ N = -\frac{\ln \left(1 – 0.2\right)}{\ln(1+0.005)} = -\frac{\ln(0.8)}{\ln(1.005)} $$
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Determine the Period:
Solving the equation yields $N$ of approximately $\mathbf{44.69}$ periods (or months), meaning the loan is paid off in just under 45 months.
Frequently Asked Questions (FAQ)
A: If your periodic payment is less than the interest accrued in that period ($PMT < P \times r$), the loan balance will never decrease. The formula requires the term inside the logarithm to be positive, which is impossible if the payment is too small to cover the interest.
A: No. $N$ is the number of **periods**. If you input a monthly rate (R) and monthly payment (PMT), $N$ will be in months. You must ensure the Rate and Periods are consistent (e.g., monthly rate goes with months).
A: The longer the amortization period ($N$), the more total interest you will pay over the life of the loan. Conversely, increasing your PMT shortens $N$ and saves you substantial interest.
A: Negative amortization occurs when the PMT is less than the interest charged, causing the principal loan balance to increase over time instead of decrease. This calculator prevents that scenario during the N calculation.