# Average annual total return

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## Average annual total return

As investors use the term, the return an investment provides over a period of time, expressed as a time-weighted annual percentage. Sources of returns can include interest, dividends, returns of capital, and capital appreciation. The rate of annual return is measured against the principal amount of the investment and represents a geometric mean rather than a simple arithmetic mean.

Annual return is the de facto method for comparing the performance of investments with liquidity, which includes stocks, bonds, funds, commodities, and some types of derivatives.

US mutual funds report the average annual compounded rates of return, for 1-year, 5-year and 10-year periods as the "average annual total return," for each fund. The following formula is used:

• P(1+T)n = ERV

Where:

• P = a hypothetical initial payment of \$1,000.
• T = average annual total return.
• n = number of years.

ERV = ending redeemable value of a hypothetical \$1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion). [1]