How to use this calculator
Choose Cash Flow when you know the starting and ending balances plus the dates of deposits or withdrawals. Enter activity amounts as positive numbers, then select Deposit or Withdraw to set their direction. Every activity date must fall between the starting and ending dates.
Choose Return Series when you know an annual return rate for each holding period. Enter each period's years and months separately; the periods can have different lengths. A return of 10% for six months means six months at a 10% annual rate, not a 10% gain over those six months. This tool reports compounded and annualized returns, rather than an arithmetic average of the percentages.
Examples
Three annual rates with different holding periods
Enter 10% for 1 year 2 months, −2% for 5 months, and 15% for
2 years 3 months. The growth factor is
1.10^(14/12) × 0.98^(5/12) × 1.15^(27/12) ≈ 1.5178.
An initial $100 therefore becomes $151.78, a cumulative return of
51.78%. The 46-month holding period gives an annualized return of
1.5178^(12/46) − 1 ≈ 11.50%.
Why an arithmetic average can mislead
A 10% gain followed by a 10% loss over two one-year periods takes $100 to $110 and then $99. The arithmetic average is 0%, but the cumulative return is −1% and the annualized return is about −0.50%.
Formula
For a series, let rᵢ be each annual rate as a decimal and mᵢ its holding
period in months:
growth factor = Π(1 + rᵢ)^(mᵢ / 12)
cumulative return = growth factor − 1
annualized return = growth factor^(12 / total months) − 1
The dated mode solves the annual rate r for which discounted cash flows sum
to zero. It treats the starting balance and deposits as negative cash flows,
and withdrawals and the ending balance as positive cash flows. Each flow is
discounted by (1 + r)^(days since start / 365.25).
Method and limits
The dated mode is a money-weighted annualized return: its answer depends on when deposits and withdrawals occur. It can differ from a time-weighted portfolio return and, with cash flows that change sign more than once, may be missing or ambiguous. The series mode compounds the entered annual rates over their stated holding periods; it assumes no cash flows within those periods and does not average the percentages arithmetically.