How this calculator works
This geometric return links one beginning value to one ending value without intervening deposits or withdrawals. You can also start with a total return percentage. Reverse modes recover a missing endpoint or the time needed at a constant annual rate. A zero ending value represents a total loss; a finite time cannot be inferred from a zero or -100% annual rate.
Formula
R = E/B - 1; a = (1 + R)^(1/t) - 1; E = B(1+a)^t; B = E/(1+a)^t; t = ln(E/B)/ln(1+a). B is beginning value, E ending value and t years.
Worked example
$10,000 becoming $12,100 in two years earns 21% in total and 10% annually. A 44% total gain over two years annualizes to 20%.
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Frequently asked questions
Can this handle regular deposits?
No. Contributions change the endpoints independently of performance. Use IRR when cash-flow timing matters.
Can the annual return be negative?
Yes. A fall from $100 to $81 in two years is -10% annually.
How are months converted?
The unit selector treats twelve model months as one year. It does not count actual dates.