will need to take the geometric mean of our

ratio of final price over first price, and then subtract 1 from that.

So, in other words, we're going to take our ratio,

$130, divided by $100 and we're going to take it

to the power that reflects how many time intervals we want to have.

So, if we want to have two time intervals for

2 years, we are going to take this

to the one-half -1 is equal to

1.1402- 1 is equal to 14.02%.

So, again, notice that we get a different value for the geometric mean or

discrete annualized return of 14.02% versus the annualized

continuously compounded return of 13.12%.

When an investment is not made all at once, but

cash is invested at several different times, the metric used to evaluate

the overall return is to identify a single fixed discrete,

annual rate of return to apply to each of the payments that,

if summed, would result in the final pay out.

This value is called the internal rate of return, or IRR.