Interest Rate Calculator
Work backwards to the rate: what return turned this starting amount into that ending amount over that time?
The other time-value formulas take a rate and give you an amount.
How the interest rate calculator works
The other time-value formulas take a rate and give you an amount. This one does the reverse, which is the question people actually have: an investment went from one figure to another over some years — what rate was that?
With no contributions the answer is exact: r = (FV/PV)^(1/n) − 1, the compound annual growth rate. Add regular contributions and no closed form exists, so this solves for the rate numerically, by bisection.
The CAGR it returns is a smoothed figure. It hides the path completely: an investment that fell 40% and then tripled has the same CAGR as one that climbed steadily, and they are not the same investment.
Formula: no contributions: r = (FV/PV)^(1/n) − 1
Worked examples
| Inputs | Annual rate | Note |
|---|---|---|
| 10,000 became 25,000 in 10 years | 9.5958% | 9.596% a year |
| Doubling in 10 years | 7.1773% | 7.177% |
| With contributions along the way | 6.7017% | solved numerically |
FAQFrequently asked questions
How do I work out the rate of return?
With no contributions it is (end ÷ start)^(1/years) − 1. This page also solves the case with regular contributions, which has no closed form.
What is CAGR?
Compound annual growth rate — the single constant rate that would take the starting amount to the ending amount over the period.
Does CAGR show risk?
No. It hides the path entirely. Two investments with identical CAGR can have had wildly different journeys.
Why does adding contributions change the method?
Because the equation can no longer be rearranged for the rate, so it has to be solved numerically.
Can the rate be negative?
Yes, whenever the ending amount is below what went in.
Where these figures come from
- CFA Institute — Quantitative Methods: The Time Value of Money — the discounting, annuity and IRR conventions used here
- US Federal Reserve — Regulation Z (Truth in Lending), APR calculation — why APR includes fees where a nominal rate does not
- MoneyHelper (UK Government-backed) — the UK's free money guidance service
Last checked: September 2026. These are the standard textbook formulas; the conventions named are those of the CFA Institute curriculum and ISO 80000 usage.