Investment Return & CAGR Calculator

• CAGR for a simple investment, computed from the standard formula.
• A money-weighted (IRR) return when cash flows make CAGR invalid — solved by bisection, so it cannot diverge.
• Real return computed with the Fisher relation, not the subtraction shortcut most people use.
• Clear about the difference between measuring the past and predicting the future.

What CAGR is, and what it hides

Compound annual growth rate is the constant annual rate that would have taken your starting value to your ending value over the period.

CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1

Turning $25,000 into $48,000 over eight years gives (48,000 ÷ 25,000)^(1/8) − 1 = 8.5%.

What CAGR deliberately hides is the path. These three investments all have a CAGR of 8.5% over eight years:

• One that gained exactly 8.5% every single year.
• One that gained 40% in year one and drifted for seven years.
• One that fell 30% in year three and recovered strongly afterwards.

Identical CAGR, wildly different experiences and wildly different risk. CAGR is a summary of the endpoints, not a description of the journey — which makes it useful for comparison and dangerous as a measure of what to expect.

It also explains why the arithmetic average of annual returns is misleading. An investment that gains 50% then loses 50% has an average annual return of 0% and a CAGR of −13.4%, because $100 becomes $150 becomes $75. Losses require disproportionate gains to recover: down 50% needs up 100% to get back to level. CAGR captures that; averaging does not.

Why contributions break CAGR

Suppose you invested $10,000, then added $500 a month for five years, and now have $55,000. Applying the CAGR formula to $10,000 and $55,000 gives 40.7% a year — which is obviously wrong, because most of that $55,000 is money you put in rather than growth.

When cash moves in or out, you need a return that accounts for when each dollar arrived. That is the internal rate of return: the discount rate at which the present value of all cash flows equals zero.

Find r such that:

  Σ  CFₜ ÷ (1 + r)^t  =  0

where CFₜ is each cash flow (negative going in, positive coming out)
and t is the time in years from the start.

There is no closed-form solution, so it has to be found numerically. This calculator uses bisection rather than Newton-Raphson: it is slower but it cannot diverge or oscillate, which matters when the inputs can be anything a user types. If no root exists — because all the cash flows have the same sign, for instance — it says so rather than returning a meaningless figure.

The moment you enter a contribution or withdrawal above, the headline figure switches to this money-weighted return and a notice explains why.

Time-weighted and money-weighted returns

These are two different questions and both have legitimate answers.

Time-weighted return removes the effect of when money went in and out. It measures the performance of the investment itself, which is why funds and managers report it — they do not control your deposit timing, so it would be unfair to judge them on it.

Money-weighted return (what this calculator computes) includes the timing effect. It measures your experience of the investment.

The two can differ substantially. If you happened to invest heavily just before a strong run, your money-weighted return will exceed the fund's reported figure. If you added most of your money just before a fall, it will be lower. Neither number is wrong; they answer different questions. When a fund's factsheet and your own account statement disagree, this is usually why.

Nominal and real return

A nominal return tells you how many more dollars you have. A real return tells you how much more you can buy.

The common shortcut — subtract inflation from the nominal return — is an approximation that drifts at higher rates. The exact relationship is the Fisher equation:

real return = [ (1 + nominal) ÷ (1 + inflation) ] − 1

At 8.5% nominal and 2.5% inflation, subtraction gives 6.0% and the exact formula gives 5.85%. A small difference over one year; over thirty years of compounding, not small. This calculator uses the exact form.

Real return is the number that matters for any long-horizon decision. An investment returning 8% while inflation runs at 9% is losing purchasing power despite showing a gain, and a plan built on the nominal figure will fall short.

Comparing investments honestly

Some conditions for a comparison to mean anything:

• The same period. Different start and end dates produce different answers, sometimes dramatically. Choosing the period after seeing the results is how most misleading performance claims are constructed.
• Total return, not price return. An index that excludes dividends understates returns substantially over long periods. Most quoted index levels are price-only.
• After fees. A return quoted before fees is not a return you could have earned.
• Adjusted for risk. A higher return achieved with much greater volatility is not straightforwardly better. This calculator does not compute risk-adjusted measures, but the comparison is incomplete without at least considering it.
• Long enough to mean something. A 30% return over one year tells you very little about the process that produced it. Three-year records are weak evidence; ten-year records are better; and even those are substantially influenced by which decade they cover.

Common mistakes

Using CAGR when you have been contributing. The most common error, and it produces figures that are wildly too high. The calculator switches automatically.

Averaging annual returns. The arithmetic mean overstates compound growth whenever returns vary. Use CAGR.

Comparing price returns with total returns. Dividends compound. Excluding them changes long-run figures substantially.

Ignoring inflation. Especially over long periods, where the difference between nominal and real is the difference between a plan working and not working.

Extrapolating a short record. The projection table in the results applies the measured rate forward, and is labelled as illustrative for exactly this reason. A three-year CAGR is not a forecast.

Forgetting externally paid fees. Advisory fees deducted from a separate account do not reduce the ending value, so they are invisible to this calculation. Subtract them yourself if they apply.

Frequently asked questions