What This Calculator Does
This calculator finds the interest rate of a loan or investment when you already know the principal (loan amount), the number of periods (loan term), and the periodic payment amount.
How It Works
We use the standard Time Value of Money (TVM) equation and solve for the interest rate using numerical methods (Newton-Raphson iteration) because there is no simple closed-form solution for the rate.
The core TVM equation used:
PV × (1 + r)n + PMT × [((1 + r)n − 1) / r] + FV = 0
Where we solve for r (periodic interest rate).
Key Concepts
- Interest Rate: The cost of borrowing money or the return on an investment, expressed as an annual percentage rate (APR).
- Amortization: The process of paying off a loan over time through regular payments that cover both principal and interest.
- Total Interest Paid: The sum of all interest portions of your payments over the life of the loan.
Tips
- A lower interest rate significantly reduces the total amount you pay over the life of the loan.
- Even small differences in interest rate (e.g., 0.5%) can save thousands of dollars on large loans.
- Always compare the APR, not just the monthly payment, when shopping for loans.