For example, if an investment fund claims to have produced a 10% annual compound return over the past five years, this means that at the end of its fifth year, the fund's capital has grown to a size equal to what it would be if the funds on hand at the beginning of each year had earned exactly 10% by the end of each year.
In other words, suppose you started with an initial investment of $1,000. If you multiply 1,000 by 1.1 five times, you will end up with about $1,611. If an investment of $1,000 ended up being worth $1,611 by the end of five years, the investment could be said to have generated a 10% annual compound return over that five-year period.
However, this does not mean that the investment actually appreciated by 10% during each of the five years. Any pattern of growth that led to a final value of $1,611 after five years would equate to a 10% annualized return. Suppose the investment earned nothing for the first four years, and then earned $611 in its last year (a 61.1% return for the year). This would still equate to a 10% annual compound return over the five-year measurement period, since the final amount is still equal to what the $1,000 would have grown to if it had appreciated by a steady 10% each year.