XIRR

XIRR (extended internal rate of return) is the single yearly rate at which every amount you put in, compounded from its own date, grows to exactly what you have now. It is the right measure whenever money went in at more than one time, because each rupee is credited only for the time it was actually invested.

It has no formula; it is found by trial, adjusting the rate until the dated cash flows balance. A spreadsheet's XIRR function does the same thing.

With a single purchase and no further flows, XIRR equals CAGR. With later top-ups, CAGR computed on the total invested overstates the return, because it treats the last rupee as if it had been invested from the first day.