Compound Interest Rate Calculator
Solve for the implied compound annual interest rate given an initial value, final value, and number of years.
How to use this tool
- Enter present value (initial amount), future value (final amount) and number of years in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your annual compound interest rate and the full breakdown beneath it.
Formula
r = (FV / PV)1/n − 1
Where r = annual compound rate, FV = future value, PV = present value, n = number of years.
How it works
This calculator inverts the standard compound growth formula FV = PV × (1 + r)n to solve for the unknown annual rate r. The result is equivalent to the Compound Annual Growth Rate (CAGR), the single constant rate that would grow the initial value into the final value over the given period.
The calculation assumes annual compounding with no intermediate cash flows. It does not account for taxes, fees, inflation, or irregular contributions.
Worked example
$1,000 growing to $2,000 in 7 years
- PV = $1,000, FV = $2,000, n = 7 years. Growth multiple = 2000 / 1000 = 2.0.
- r = 2.0^(1/7) − 1. Compute 2^(1/7): ln(2)/7 = 0.693147/7 = 0.099021; e^0.099021 ≈ 1.10409.
- r = 1.10409 − 1 = 0.10409, i.e. 10.409% per year.
- Verify: 1000 × 1.10409^7 ≈ 1000 × 2.000 = $2,000. ✓
Annual compound rate ≈ 10.409%.
Key terms
- CAGR
- Compound Annual Growth Rate — the constant annual rate at which a quantity grows from its initial to its final value over a specified period.
- Growth Multiple
- The ratio of final value to initial value (FV / PV), indicating how many times the original amount has grown.
- Compounding
- The process where returns are reinvested so that gains in each period generate additional gains in subsequent periods.
- Implied Rate
- The interest or growth rate inferred from observed initial and final values over a known time horizon.