Finding the average annualized rate of return

To find the annualized rate of return for an aggregate of transactions:

Let x1 = a1/b1 * 100 * 1/t1 ........ (1)

and x2 = a2/b2 * 100 * 1/t2 ....... (2)

where x = annualized rate of return; a = actual value of return; b = actual amount invested; t = time for which invested.

Equation (2) can be written as

x2 = (a2*b1/b2)/b1 * 100 * 1/t2

So, we can assume that b1 amount of money has been invested for (t1 + t2) amount of time and the actual return was (a1 + a2*b1/b2)

Therefore, the average annualized rate of return

= (a1 + a2*b1/b2)/b1 * 100 * 1/(t1 + t2)

= (a1/b1 + a2/b2) * 100 * 1/(t1 + t2)

= (x1*t1 + x2* t2) / (t1 + t2)