Mr. Sterling is a recognized expert in loan servicing and amortization modeling, with 20+ years of experience in the banking sector.
The **Loan Repayment Schedule Calculator** determines the required **Periodic Payment (PMT)**, **Interest Rate (R)**, or **Loan Term (N)** for an amortized loan. It generates a detailed repayment schedule (amortization table) showing how each payment is split between principal and interest. **Input any three of the four core variables** to solve for the missing one.
Loan Repayment Schedule Calculator
Loan Amortization Formulas
The core loan payment (PMT) calculation for a fixed-rate, fixed-term loan uses the Present Value of Ordinary Annuity (PVOA) formula, where the principal (P) equals the present value (PV):
Where $i = \frac{R}{1200}$ (Monthly Interest Rate) and $n = N \times 12$ (Total Monthly Payments).
Formula Source: Investopedia: Amortization Formula
Variables Explained
The key components of the Loan Repayment Schedule calculation are:
- Loan Principal (P, F): The initial amount of money borrowed ($).
- Periodic Payment (PMT, P): The fixed amount paid each period, typically monthly ($).
- Annual Interest Rate (R, V): The annual percentage rate (APR) of the loan (%).
- Loan Term (N, Q): The total duration of the loan in years.
Related Loan Calculators
Use these related tools to manage your debt and understand loan structures:
- Loan Amortization Period Calculator
- Loan-to-Value (LTV) Ratio Calculator
- Simple Interest Calculator
- Debt-to-Income (DTI) Ratio Calculator
What is a Loan Repayment Schedule?
A **Loan Repayment Schedule**, also known as an amortization schedule, is a table detailing each periodic payment due on an amortized loan. It breaks down how much of each payment goes toward the interest owed and how much goes toward reducing the principal balance. This schedule is critical because, for most loans, the initial payments are predominantly interest, with the principal repayment increasing toward the end of the loan term.
The amortization process ensures that the loan is fully paid off by the final scheduled payment. Understanding this schedule allows borrowers to analyze the cost of borrowing (total interest paid) and the impact of making extra principal payments to shorten the loan term.
How to Generate a Loan Repayment Schedule (Example)
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Determine the Monthly Rate and Payments:
Assume a $\mathbf{\$10,000}$ loan at an $\mathbf{8\%}$ annual rate for $\mathbf{2}$ years. The monthly rate $i = 0.08/12 \approx 0.006667$. The total payments $n = 2 \times 12 = 24$.
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Calculate the Fixed Monthly Payment (PMT):
Using the PMT formula, the required monthly payment is calculated to be approximately $\mathbf{\$452.27}$.
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Calculate Interest for Period 1:
Interest = Principal ($\$10,000$) $\times$ Monthly Rate ($0.006667$) = $\mathbf{\$66.67}$.
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Calculate Principal Repaid in Period 1:
Principal Repaid = PMT ($\$452.27$) – Interest ($\$66.67$) = $\mathbf{\$385.60}$.
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Calculate Remaining Balance:
Balance = Previous Balance ($\$10,000$) – Principal Repaid ($\$385.60$) = $\mathbf{\$9,614.40}$.
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Repeat:
Repeat steps 3-5 for all 24 periods, using the new remaining balance as the principal for the next calculation.
Frequently Asked Questions (FAQ)
A: Amortization is the process of gradually paying off debt over a fixed period of time through regular installments. Each installment consists of both principal and interest, structured so the debt is fully extinguished by the end of the term.
A: When you make an extra payment designated for principal, it immediately reduces the outstanding balance. Since future interest is calculated on the remaining principal, this reduces the total interest paid and shortens the loan term significantly.
A: Interest is calculated on the largest outstanding principal balance at the start of the loan. As the principal reduces with each payment, the interest portion of the fixed payment decreases, and the principal portion increases.
A: Yes, the calculator is designed to solve for the missing rate (R) using iterative numerical methods, making it a powerful tool for verifying loan quotes or solving for unknown variables.