CAGR Reverser
Estimate the fractional years for a starting value to reach a target under a constant positive annual growth rate.
How it works
Enter positive starting and target values in the same currency or unit, then enter a positive annual growth rate as a percentage. The calculator solves the compound growth equation for fractional years. If the target is already met, it reports zero years and displays the current value.
The table shows annual values when the horizon is 100 years or less. For a longer horizon, it uses up to 100 evenly spaced sample intervals, then includes the exact target point and the next whole year point. The target point can fall between annual values, so its value may differ from the next row.
With a starting value of 10,000, target of 20,000, and annual growth rate of 7%, the equation gives about 10.2448 years. The exact target point is 20,000; the year 11 projection is about 21,048.52. The focused calculation test verifies this example.
Use the output to compare constant rate scenarios. Actual returns vary over time, and the model does not include contributions, withdrawals, fees, taxes, or inflation. Recalculate with updated values when the starting balance changes.
Step by step
- Enter the starting value and target in the same unit.
- Enter a positive annual growth rate.
- Review the fractional timeline and projection points.
Worked example
For a starting value of 10,000, a target of 20,000, and a constant annual growth rate of 7%, the target time is about 10.24 years.
The projection includes an exact target point at about year 10.24 with value 20,000, followed by the whole year 11 point at about 21,048.52. The test suite checks the same inputs and values.
When to use this calculator
Use this calculator to compare how different constant positive annual growth assumptions change the time from a starting value to a target.
Use a cash flow model when your plan includes recurring deposits or withdrawals. This tool isolates compound growth from one starting value.
Common input mistakes
Do not enter a percentage as a decimal. For example, enter 7 for 7%, not 0.07. Make sure the start and target use the same currency or unit.
Do not treat the fractional year as a date or assume the entered rate will persist. The projection is a constant rate scenario and excludes cash flows and investment costs.
Formula
years = ln(targetValue / startValue) / ln(1 + CAGR / 100)
valueAtYear = startValue × (1 + CAGR / 100) ^ year
If targetValue is less than or equal to startValue, years = 0.
The model assumes a constant positive annual growth rate compounded once per year. Values must use the same currency or unit. The calculator does not convert currencies. Fractional years are mathematical estimates rather than dated forecasts.
Assumptions and limits
The calculation assumes a constant positive annual growth rate with annual compounding. Actual investment returns fluctuate and are not guaranteed. The model excludes contributions, withdrawals, inflation, fees, taxes, and account specific rules. Starting value, target, and rate must be finite and positive, and use the same currency or unit. Longer horizons use up to 100 sample intervals, plus the exact target and next whole year points. The result is not a forecast or financial advice.
Key terms
- Annual growth rate
- The compound annual growth rate entered as a percentage for this scenario.
- Fractional years to target
- The time in years when the modeled value reaches the entered target under a constant growth assumption.
- Projection point
- A calculated value at a whole or sampled year, plus an exact point when the target is reached.
Related tools
CAGR Finder calculates an annualized rate from two historical values. Total Return Calculator can include distributions in a historical return calculation. This tool instead models a constant rate entered by you.
For a contribution plan, use a calculator that includes recurring deposits. This calculation has no additions or withdrawals, so it only describes growth from the starting value.
FAQ
What does the CAGR Reverser calculate?
Enter the starting value, target value, and positive annual growth rate. The calculator solves for the time at which constant annual compounding reaches the target. If the target is already at or below the starting value, it reports zero years and shows the current value.
How is the time to target calculated?
It divides the natural logarithm of target divided by start by the natural logarithm of one plus the annual rate as a decimal. The answer is fractional years, not a guaranteed calendar date. The projection marks the exact target point and, when there is one, the next whole year value.
How does changing the growth rate affect the result?
A higher positive rate shortens the modeled time because growth compounds on an increasing base. The relationship is nonlinear. Compare scenarios as assumptions, since a small rate change can materially change a long horizon.
What growth rate should I enter?
There is no universally realistic rate for every portfolio or period. The result depends entirely on the rate you enter and assumes it remains constant. Consider a range of scenarios and account for inflation, fees, taxes, and volatility separately if those are relevant to your plan.
Can this estimate a FIRE or savings goal timeline?
You can compare a starting portfolio with a future goal under a constant growth assumption. The model does not include new savings, withdrawals, inflation, or a changing return path, so use it only for a static growth scenario.
Related tools
CAGR Finder works backward from historical values to calculate an annualized rate. Total Return Calculator includes distributions in historical performance. Use this calculator for a forward constant rate scenario without cash flows.