Workspace
The calculator's own fields, action and results arrive with the verified pack when you load it. Nothing is computed in this page.
Performance measurement · after the fact
Investment return: total, annualized, net and real
Audit a finished investment: from its starting and ending value over a span of years, the total return, the annualized pace, and that pace net of fees and net of inflation.
Verified engine
What the engine returns
Read the four outputs downward. The total return is the headline and looks enormous; the annualized pace beneath it is modest and is the honest speed. With the fee entered, the net pace steps down by exactly the fee. With inflation entered, the real pace at the bottom steps down again — and by slightly more than plain subtraction would predict, because erosion compounds.
Inputs the result is built from
Starting value
Ending value
Years elapsed
Annual fee or expense rate
Annual inflation rate
How the result is derived
MethodThe ratio of ending to starting value gives the total return; its geometric annualization over the years elapsed gives the annual pace; the fee rate is subtracted from that pace; inflation is then removed by compounding the net rate against the inflation rate.
StandardCompound annual growth rate and total-return relations
GuardA starting value at or below zero is refused. The return is a ratio against the starting value, and a journey from nothing has no measurable pace — the pack’s declared vectors include exactly this refusal.
Reading a headline return down the ladder
The total return is the crowd-pleaser and the least informative rung. Money that doubles over a long holding shows a total return that sounds spectacular, while the annual pace that produced it is modest. The annualized figure is a geometric average — the steady yearly rate that would have produced the same journey — and it is always below what dividing the total by the years would suggest, because compounding does part of the work.
Fees come off the annual pace point for point. An ongoing management charge is levied every year regardless of performance, so the pace net of fees is simply the annual pace with the fee rate subtracted — a small-looking number that repeats annually, which is exactly how small numbers become large ones.
Inflation is not subtracted; it is divided out. Buying power compounds against you the same way returns compound for you, so the real pace comes from compounding the fee-net rate against the inflation rate. The result sits slightly below what naive subtraction would give, and the gap widens as either rate grows.
Everything here is a measurement of one window, not a property of the investment. Move the start or end date and every rung of the ladder moves with it. A pace measured from a low point to a high point flatters; the same holding measured across a different window can tell the opposite story. The arithmetic is exact about the window it is given and silent about every other.
The ratio of ending to starting value gives the total return; its geometric annualization over the years elapsed gives the annual pace; the fee rate is subtracted from that pace; inflation is then removed by compounding the net rate against the inflation rate.
When this calculation is used
- Judging whether a holding you sold, or could sell, actually beat what it cost to own.
- Translating a many-year total return quoted in marketing into an annual pace you can compare against alternatives.
- Seeing what an ongoing fee did to a finished result, rather than to a hypothetical one.
- Converting a nominal track record into buying-power terms before drawing any conclusion from it.
Worked example
Take a holding that doubled over a long stretch of years, first with no costs entered, and then the same doubling with an ordinary management fee and everyday inflation added in.
Read the four outputs downward. The total return is the headline and looks enormous; the annualized pace beneath it is modest and is the honest speed. With the fee entered, the net pace steps down by exactly the fee. With inflation entered, the real pace at the bottom steps down again — and by slightly more than plain subtraction would predict, because erosion compounds.
Notice which rungs move and which do not: the total and the gross pace belong to the investment itself, while the net and real rungs belong to its costs and its era — the fee and inflation entries change only the bottom half of the ladder. Every figure shown is computed by the verified engine after the page loads, and the relation it runs is the one exercised by the signed pack’s own declared test vectors; the page itself holds no answers.
What each input represents
Starting value
What the holding was worth at the start of the window being measured. It must be a positive amount — the whole calculation is a ratio against this figure, and a ratio against nothing is not a return.
Ending value
What the holding was worth at the end of the window, after any growth or loss. An ending value below the starting value is a perfectly valid input; the ladder simply reads downward in the negative.
Years elapsed
The length of the window, in years, over which the change happened. This is what turns a total into a pace: the same doubling is impressive over few years and unremarkable over many.
Annual fee or expense rate
The ongoing yearly charge for holding the investment, as a percentage. Optional — leaving it out measures the gross pace. It is subtracted from the annual pace directly, because it is charged every year whether the holding grew or not.
Annual inflation rate
The yearly pace at which prices rose over the same window, as a percentage. Optional — leaving it out keeps the answer nominal. It enters by ratio rather than subtraction, because buying power erodes by compounding, not by instalments.
Assumptions and limits
- The window is a single unbroken holding with no deposits or withdrawals in between — this measures a lump sum’s journey, not a contribution stream.
- The fee is a constant annual rate applied to the whole window and subtracted from the annual pace.
- Inflation is a constant annual rate over the same window, removed by ratio rather than subtraction.
- The annualized figure is a geometric average: the steady rate that reproduces the endpoint, not the average of each year’s individual result.
- Taxes on gains are outside the calculation entirely.
What the guards protect against
- A starting value at or below zero is refused. The return is a ratio against the starting value, and a journey from nothing has no measurable pace — the pack’s declared vectors include exactly this refusal.
- A span of zero or negative years is refused: a pace requires elapsed time to be a pace at all.
- The fee and inflation rates are bounded to realistic ranges, and the ending value cannot be negative — a holding can end worthless but not below worthless.
Provenance
Compound annual growth rate and total-return relations
The ratio of ending to starting value gives the total return; its geometric annualization over the years elapsed gives the annual pace; the fee rate is subtracted from that pace; inflation is then removed by compounding the net rate against the inflation rate.
An educational reference for interpreting past performance — not financial advice, and a measured past pace is no indication of a future one. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.