Loan Calculator
Estimate fixed-rate monthly payments, total interest costs, and repayment schedules with a transparent amortization breakdown.
Fixed-Rate Installment Math
Calculates standard amortizing loan payments based on fixed nominal interest rates.
Full Schedule Transparency
View both yearly summaries and monthly breakdowns showing exact principal and interest split.
Zero Balance Guarantee
Normalized final period payment ensures the loan balance resolves to exactly zero.
How Fixed-Rate Loan Amortization Works
An amortizing loan is structured so that you pay a fixed amount each month over a predetermined number of periods. Each payment is split between interest charged on the remaining balance and principal reduction:
1. Monthly Payment Formula
For annual rate r > 0, monthly payment is derived by:
M = P × [r(1 + r)^n] ÷ [(1 + r)^n − 1]
Where P = Principal, r = monthly rate, and n = total months.
2. Period-by-Period Amortization
Every month, the interest charge is computed on the current balance:
Interest = Balance × r Principal = Payment − Interest
The remainder of the monthly installment reduces your balance.
Worked Loan Payment Examples
Example 1: $10,000 at 6.00% for 5 Years (60 Months)
Monthly rate r = 0.06 ÷ 12 = 0.005. Monthly payment = $193.33. Total interest paid over 5 years is $1,599.68, resulting in a total repayment of $11,599.68.
Example 2: $20,000 at 8.00% for 5 Years (60 Months)
Monthly payment = $405.53. Total interest paid is $4,331.67, for a total repayment of $24,331.67.
Example 3: $12,000 at 0.00% for 1 Year (12 Months)
Zero-interest loan: $12,000 ÷ 12 = $1,000.00/month with $0.00 total interest.
Important Boundaries & Disclaimers
- • Nominal Rate vs APR: This tool uses a nominal annual interest rate. It does not calculate APR, which may include interest plus applicable lender fees or finance charges, depending on the loan and jurisdiction.
- • Fixed Monthly Only: V1 supports fixed-rate monthly amortization only. It does not model weekly payments, interest-only loans, or balloon payments.
- • Taxes & Escrow: Property taxes, homeowner's insurance, and private mortgage insurance (PMI) are not included.
- • Mathematical Estimator: Formulexa is not a lender or financial advisor. Refer to your lender's official Loan Estimate and Closing Disclosure documents for binding terms.
Borrowing & Amortization Guides
How Loan Payments Are Calculated
Step-by-step breakdown of the standard amortization equation and periodic interest rates.
Amortization Schedules Explained
How interest and principal proportions shift over the course of a multi-year loan.
Principal vs Interest
Learn how principal reduction lowers the outstanding balance while interest pays the cost of borrowing.
Frequently Asked Questions
How is a monthly loan payment calculated?
What is the difference between interest rate and APR?
Why do earlier payments contain more interest than principal?
Does this calculator model balloon payments or adjustable rates?
Can I use this for auto, personal, or student loans?
Methodology & Regulatory Definitions
Formulexa adheres to standard mathematical amortization formulas and terminology published by consumer financial regulatory authorities:
- Consumer Financial Protection Bureau (CFPB): “What is the difference between a loan interest rate and the APR?” Explains that interest rate is the cost of borrowing principal while APR includes additional finance charges and applicable fees.
- Consumer Financial Protection Bureau (CFPB): “What is amortization and how could it affect my auto loan?” Explains fixed monthly payment allocations between interest and principal over the loan term.
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