Rate of Return Calculator

Total return over the whole holding period compares end value to start value:

$R = \frac{V_{\text{end}} - V_{\text{begin}}}{V_{\text{begin}}}$

It says nothing about how long that took, so a 51% total return over four years and over twenty years look identical. Annualising fixes that. The compound annual growth rate is

$CAGR = \left(\frac{V_{\text{end}}}{V_{\text{begin}}}\right)^{1/t} - 1$

with $t$ in years (fractions allowed). $CAGR$ is the single constant rate that would have produced the same ending value — it is a geometric average, not the arithmetic mean of yearly returns, and it is always the smaller of the two whenever returns vary.

Real return strips out inflation. Use the exact relation, not subtraction:

$r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + \pi} - 1$

where $\pi$ is the inflation rate over the same period. At small rates $r - \pi$ is a decent approximation, but it drifts as either rate grows.

The accumulation formula

A starting balance plus a fixed contribution each period, at a periodic rate $i = r/n$ over $N = nt$ periods:

$FV = P(1+i)^N + C \cdot \frac{(1+i)^N - 1}{i}$

The first term compounds what you already have; the second is the future value of the contribution stream, since each contribution compounds for a different length of time. Contributions at the start of each period multiply the second term by $(1+i)$.

Withdrawals, in reverse

Drawing $W$ per period from a balance $B$ runs the same machinery backwards:

$B = W \cdot \frac{1 - (1+i)^{-N}}{i}$

Solve for $N$ to find how long a balance lasts at a given withdrawal, or for $W$ to find the level withdrawal a balance supports over $N$ periods.

Doubling and required return

$t = \frac{\ln 2}{\ln(1+r)}, \qquad r = \left(\frac{V_{\text{target}}}{V_{\text{now}}}\right)^{1/t} - 1$

Every projection here is arithmetic on a rate you supply. Markets do not deliver a constant return, and this page neither forecasts one nor recommends any course of action — it shows what a chosen assumption implies.

• Averaging yearly returns arithmetically: $+50\%$ then $-50\%$ averages to $0\%$ but leaves you at $0.75$ of where you started. The CAGR is $\sqrt{0.75} - 1 \approx -13.4\%$.
• Dividing total return by the number of years: $51.2\%$ over 4 years is not $12.8\%$ a year. Take the fourth root of the growth factor instead.
• Subtracting inflation: use $(1+r)/(1+\pi) - 1$. At 7% and 3% the exact real return is $3.8835\%$, not $4\%$.
• Ignoring contributions when measuring return: a balance that grew because you paid money in did not earn that return. Compare like with like, or use a money-weighted measure.
• Mismatching $i$ and $N$: monthly contributions need $i = r/12$ and $N = 12t$. Changing one without the other is the most common arithmetic error here.
• Reading a projection as a forecast: the output is only as good as the constant rate assumed, and real returns are neither constant nor knowable in advance.