📖 The story
A fund unit rose from $75 to $240 over 9 years. The salesperson advertises the big total gain – but customer Paula wants to know the real annual return.
ℹ Lump-sum investment, annual view.
Topics › Mutual Funds & Securities › Performance is not the same as return
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Mutual Funds & Securities
Performance is not the same as return
Change any number and press "Calculate" – or use "Type in" on the right to watch it entered step by step.
What you learn
Performance is not return: a high total rise sounds spectacular, yet the real annual return lies far below it because of compound interest. Always have the return named to you, not the performance.
In short: The true return computed with compounding lies far below the apparent average performance – customers should always be told the return.
Formula
i = (FV/K0)^(1/n) − 1
With the example numbers
i = (240/75)1/9 − 1 = 13.80 %
How to read the formula
Extracting the return from the starting and ending value means taking the n-th root of the ratio: i = (FV/K₀)^(1/n) − 1. The root spreads the total gain evenly across all years – that is the true average return, not the naive total gain divided by the years.
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