What return do you need? CAGR required for 2x to 10x

Working backwards from the number

Most return tables start with an amount and a rate and tell you what you end up with. Goals work the other way round: you have a target, and the question is what rate it needs. A table of required returns is a quick way to see whether a goal is plausible before you plan around it.

The idea is the same as in CAGR vs absolute return, run in reverse. The formula is:

Required return = (target ÷ start)^(1 ÷ years) − 1

It applies to a single amount invested once and left alone.

The table

The multiple is the final value divided by the amount you start with. The figures are the compound annual return needed, rounded to one decimal place.

Two things stand out. The required rate falls steeply as time rises: a 5x in 5 years needs 38% a year, while a 5x in 20 years needs 8.4%. And the same multiple needs very different returns over different horizons, which is why time is the cheapest input you have.

Three worked examples

₹10 lakh to ₹25 lakh in 10 years. The multiple is 2.5. 2.5^(1/10) is about 1.096, so you need about 9.6% a year. Between the 2x column (7.2%) and the 3x column (11.6%) at 10 years, which is where you would expect it.

₹5 lakh to ₹1 crore in 20 years. The multiple is 20. 20^(1/20) is about 1.1616, so you need about 16.2% a year. That is above the 10x figure for 20 years (12.2%) because the multiple is twice as large. A target this far out of reach usually calls for a bigger starting amount or a longer time, not a hope for a better rate.

₹20 lakh to ₹50 lakh in 7 years. The multiple is 2.5 again, but over a shorter horizon. 2.5^(1/7) is about 1.140, so you need about 14.0% a year, against 9.6% over 10 years for the same multiple. Three fewer years add 4.4 percentage points to the required return.

What the shortfall looks like

Suppose the first example earns 8% a year instead of 9.6%. ₹10 lakh at 8% for 10 years becomes ₹10 lakh × 1.08¹⁰, about ₹21.6 lakh, which is ₹3.4 lakh short of ₹25 lakh. Over a 10-year horizon, a 1.6-point gap in the annual return costs about 14% of the target.

That is why a plan built on a single required rate is fragile. If the rate needed is at the top of what you would expect, small shortfalls turn into large gaps in the final amount.

How to use the table

1. Pick your multiple and your years. Find the cell or work it out with the formula.
2. Ask if the rate is plausible. Compare it with what the relevant fund category has returned over similar periods. The screener and individual fund pages show return history by category and fund; past returns do not guarantee future ones.
3. If it is not, change an input. A longer horizon, a larger start or a smaller target all reduce the required rate. The table shows which of these helps most.
4. Allow for inflation. The table is in rupees. A 2x over 12 years sounds like growth, but at 6% inflation the buying power is about unchanged. The rule of 72 explains the doubling time.

What the table leaves out

• Monthly investing. A SIP spreads money over the years, so the effective time is shorter than the full horizon. The goal calculator and the years-to-goal calculator handle regular contributions.
• Tax. Returns after tax are lower than before-tax returns, so the pre-tax rate you need is higher.
• Volatility. A return of 10% a year on average is not 10% each year. The order of returns matters if you are withdrawing money.
• Costs. Fund expenses are already reflected in a fund's net return, but not in a general plan.

To check a past return rather than a required one, the CAGR calculator takes a start value, an end value and the years.

Required returns are arithmetic on the numbers you enter, not forecasts of what any investment will earn. Past returns do not guarantee future returns.