# Compound Annual Growth Rate (CAGR)

## What it is:

The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.

The formula for CAGR is:

CAGR   =   ( EV / BV)1 / n - 1

where:

EV = Investment's ending value
BV = Investment's beginning value
n   = Number of periods (months, years, etc.)

## How it works (Example):

Let's assume you invest \$1,000 in Fund XYZ for five years. The year-end value of the investment is listed below for each year.

Year    Ending Value
1             \$   750
2               1,000
3               3,000
4               4,000
5               5,000

We can calculate the CAGR of the investment as:

CAGR = ( 5,000 / 1,000)1/5 - 1 = .37973 = 37.97%

TIP: If you are using a financial calculator, use the yx button to raise ( 5,000 / 1,000) to the power of 0.20 (since 1 / 5 = 0.20 ).

[Our easy to use CAGR Calculator can help you project the CAGR needed to achieve your investment goals or measure the return on existing investments.]

## Why it Matters:

Although average annual return is a common measure for mutual funds, CAGR is a better measure of an investment's return over time.

For example, consider Year 1 and Year 2 of our hypothetical investment in Fund XYZ.  At the end of Year 1, the portfolio value had fallen from \$1,000 to \$750 for a return of -25% [ (750 - 1,000) / 1,000 ]. By the end of Year 2, the portfolio value had grown by +33% [ (1,000 - 750) / 750 ].

Averaging the Year 1 and Year 2 returns over two years gives us an average return of 4% [ (-25 + 33) / 2 ], but that doesn't accurately reflect what has happened. We began with \$1,000 and ended with \$1,000, which is a return of 0%.

This example shows why CAGR is a better measure of return over time. Average annual return ignores the effects of compounding and it can overestimate the growth of an investment. CAGR, on the other hand, is a geometric average that represents the one, consistent rate at which the investment would have grown if the investment had compounded at the same rate each year.

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