Interest Rate Calculator
Uncover the effective annual interest rate (EAR) hidden inside given installment terms.
Parameters & Inputs
Summary & Breakdown
About the Interest Rate Calculator
Lenders frequently disguise true borrowing costs by emphasizing low monthly payment figures or flat add-on charges while omitting the genuine Annual Percentage Rate (APR).
This interest rate calculator solves for the underlying internal rate of return using numerical bisection algorithms on your loan balance and payment terms.
Knowing your genuine APR enables fair comparisons across installment agreements, credit lines, and peer-to-peer offers.
How the Calculations Work
Solves for the monthly periodic rate r in the annuity equation using numerical bisection approximation.
P = PMT * [1 - (1 + r)^(-n)] / r, APR = r * 12, EAR = (1 + r)^12 - 1
Variables & Definitions
- P: Principal funded balance
- PMT: Regular monthly payment installment
- n: Total payment periods in months
Financing $20,000 with a monthly payment of $480 across 48 months: Numerical solver finds periodic rate r = 0.00585 (0.585% per month). Multiplying by 12 gives an annual APR of 7.02%. Effective annual rate EAR is 7.25%.
Key Terms Explained
Annual Percentage Rate (APR)
The annualized cost of borrowing expressed as a percentage rate.
Effective Annual Rate (EAR)
The genuine annual rate taking into account compounding within the year.
Internal Rate of Return (IRR)
The discount rate making net present value of all cash flows equal zero.
Add-on Interest
An outdated deceptive calculation charging interest on the original balance for the full term without amortization.
Practical Tips & Pitfalls to Avoid
Never accept "flat fee" loans without checking APR
Payday and short-term loans offering a "$15 fee per $100" actually carry APRs exceeding 390%.
Compare EAR when compounding differs
The Effective Annual Rate normalizes loans with different compounding frequencies.
Account for mandatory dealer fees
Include all documentation and lender origination fees in principal to reveal the true APR.
Check truth-in-lending disclosures
US federal law mandates written disclosure of the APR on all consumer credit agreements.
Frequently Asked Questions
Because the variable r cannot be isolated algebraically, numerical bisection or Newton-Raphson approximation is used.
APR is the nominal rate (monthly rate × 12). EAR accounts for compounding: (1 + monthly rate)^12 - 1.
Average rates vary by benchmark federal rates and credit tiers, typically ranging from 5% to 8% for prime borrowers.
The interest rate applies annually. Over multi-year terms, cumulative interest accumulates across all years.
In rare macroeconomic conditions, central banks set negative rates, but consumer lending always features positive rates.