Solve for the interest rate given present value, payment, periods, and future value
This interest rate calculator solves for the unknown annual interest rate using the present value, payment amount, number of periods, and future value. It uses the Newton-Raphson method to iteratively find the rate that satisfies the time value of money equation.
Knowing the effective interest rate on a loan or investment allows you to compare offers with different terms and payment structures. This calculator is especially useful for evaluating mortgages, auto loans, and long-term investment scenarios where the rate is not explicitly stated.
The calculator uses the TVM equation: PV × (1 + r)^N + PMT × ((1 + r)^N − 1) / r = FV. It iteratively solves for the periodic rate r using Newton-Raphson, then multiplies by 12 for the annual rate.
You need at least four of the five TVM variables: present value, payment per period, number of periods, and future value. The calculator then solves for the missing interest rate using numerical iteration.
There is no closed-form algebraic solution for the interest rate in the TVM equation when payments are involved. The Newton-Raphson method provides a highly accurate approximation by iteratively refining the rate until the equation balances.
The interest rate is the annual cost of borrowing the principal amount, while APR includes the interest rate plus any fees like origination charges or closing costs. APR is always equal to or higher than the interest rate and gives a truer picture of total borrowing costs.
Even a small difference in interest rate can have a dramatic impact on total loan cost. For a $300,000 30-year mortgage, a 6% rate results in roughly $347,000 in total interest, while a 7% rate costs about $418,000 — a difference of $71,000. Shopping for the lowest rate saves substantial money.
A fixed interest rate stays the same for the entire loan term, providing predictable payments. A variable rate fluctuates with market conditions, often starting lower but carrying the risk of future increases. Fixed rates offer stability, while variable rates can save money if rates stay low.