Interest Rate Calculator
Know the start, the end and the time — but not the rate? This solver works backwards to the constant annual rate that connects them, and gives its APY equivalent.
Solving the equation backwards
Most interest problems hand you the rate. Real life hands you endpoints: money went in here, came out there, this many years later. The rate that connects them — the constant rate that would have produced exactly that journey — is what this solver extracts.
Rate = m × ((FV ÷ PV)1 ÷ (m × years) − 1), m = periods per year
Example: $10,000 became $15,000 in 5 years: the connecting rate is 8.45% nominal compounded monthly — an effective 8.79% a year. A salesperson calling that 'a 50% return' and a banker calling it 8.45% are describing the same five years.
The average hides the ride
A constant solved rate says nothing about the path: two investments with identical endpoints can have had utterly different journeys, one smooth, one a roller coaster that passed through half its value. CAGR-type figures (this is one) are for comparing outcomes, not for describing experiences.
How this is calculated
The closed-form solution for the nominal rate with the chosen compounding: rate = m × ((FV/PV)^(1/(m·t)) − 1) × 100. The APY line re-compounds that nominal rate for a year. If contributions or withdrawals happened in between, the endpoints alone cannot determine a rate — that problem needs the timing of every flow (an IRR), which this page deliberately does not pretend to solve.
Frequently asked questions
Is this the same as CAGR?
With annual compounding, yes — set the frequency to yearly and the solved rate is the CAGR. Other frequencies give the nominal rate that compounds to the same destination.
What if the ending value is smaller?
The solver returns a negative rate — a loss expressed as a yearly rate. That is a feature: it lets a shrinking investment be compared on the same scale as growing ones.
Can I solve for time instead?
Not here — but the Rule of 72 answers the most common time question (doubling), and the millionaire calculator solves time-to-a-goal with contributions included.
Why does the answer change with compounding frequency?
Because '8% nominal' means different effective growth at different frequencies. The endpoints are fixed facts; the nominal label that reproduces them depends on the compounding convention you declare.
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