Sarah specializes in personal debt management, amortization analysis, and optimizing repayment schedules for various loan types including mortgages and auto loans.
The **Loan Repayment Calculator** helps you analyze fixed-rate, amortized loans by solving for the **Loan Principal (F)**, **Monthly Payment (P)**, **Annual Rate (V)**, or **Loan Term in Years (Q)**. This flexible tool requires exactly three inputs to determine the fourth, allowing you to quickly model different financial scenarios.
Loan Repayment Calculator
Enter three values to solve for the missing one.
Loan Amortization Formulas
The calculation is based on the formula for the monthly payment of a fixed-rate loan, where payments are made monthly.
Solve for Monthly Payment (P):
P = F × [ i(1 + i)n / ( (1 + i)n − 1 ) ]
Solve for Principal (F):
F = P × [ ( (1 + i)n − 1 ) / i(1 + i)n ]
Variables Key:
i = Annual Rate (V) / 1200 (Monthly Rate)
n = Loan Term (Q) × 12 (Total Payments in months)
Formula Source: Investopedia: Loan Amortization Formula
Variables Explained
- F (Loan Principal): The initial amount of money borrowed ($).
- P (Monthly Payment): The fixed amount paid each month to the lender ($).
- V (Annual Interest Rate): The annual rate of interest charged by the lender (%).
- Q (Loan Term): The total length of the loan (Years).
Related Calculators
Analyze your loan costs and repayment options more deeply:
- Mortgage Payment Calculator (For home loans specifically)
- Loan Interest Calculator (Simple interest tool)
- Debt Consolidation Calculator (Evaluate refinancing savings)
- Amortization Schedule Calculator (See interest vs. principal breakdown)
What is Loan Repayment?
Loan repayment is the process of paying back a borrowed sum (the principal) plus the accrued interest over a specified period (the term). For most mortgages and consumer loans, this is handled through **amortization**, a method where each monthly payment remains fixed, but the proportion of that payment allocated to interest versus principal changes over time.
Early in the loan term, the majority of the payment goes toward interest, while later payments predominantly reduce the principal balance. Understanding this repayment schedule is crucial for borrowers, as it clarifies the true cost of borrowing and helps plan for accelerated repayment strategies.
How to Calculate Loan Term (Example)
Let’s find the **Loan Term (Q)** for a \$15,000 Loan Principal (F), \$300 Monthly Payment (P), and 8.0% Annual Rate (V).
- Determine Monthly Rate (i):
i = 8.0% / 1200 = $\mathbf{0.006667}$
- Apply Logarithm Formula (Solve for n):
n = [ -ln( 1 − (F × i / P) ) ] / ln(1 + i)
n = [ -ln( 1 − (\$15000 × 0.006667 / \$300) ) ] / ln(1.006667) $\approx \mathbf{57.7}$ months
- Final Term Calculation (Q):
Q = n / 12 = 57.7 months / 12 $\approx \mathbf{4.81}$ years.
Frequently Asked Questions (FAQ)
What is amortization?
Amortization is the process of paying off debt over time in fixed installments. Each payment consists of both principal and interest, ensuring the loan balance is zero at the end of the term.
Will extra payments save me money?
Yes. If extra payments are applied directly to the principal balance, they reduce the amount of principal on which future interest is calculated, drastically reducing the total interest paid and shortening the loan term.
What is a negative amortization loan?
Negative amortization occurs when the monthly payment is less than the interest charged, causing the outstanding loan principal to actually increase over time. This is dangerous and generally only seen in specific adjustable-rate mortgage (ARM) products.
Does this calculator work for mortgages and auto loans?
Yes. As long as the loan has a fixed interest rate and fixed monthly payments (amortized loan), the core financial formulas are the same, regardless of the asset being financed.