Mental Math: Growth Rates and Compounding in Interviews

Growth math is the second mental-math family interviewers reach for after percentages and multiples. The questions are never hard algebra: "revenue grows 20 percent a year for 3 years, where does it land," "how long to double at 15 percent," or "what CAGR takes 100 to 200 in 5 years." Every one of them falls to a small set of memorized factors and one rule: growth multiplies, it never adds.

TL;DR

• Compounding multiplies: two years of 20 percent growth is 1.2 × 1.2 = 1.44, so the answer is 44 percent, not 40 percent.
• Rule of 72: years to double is about 72 divided by the growth rate; the rate to double in n years is about 72 divided by n.
• Memorize five factors: 1.1² = 1.21, 1.2² = 1.44, 1.5² = 2.25, 2x in 5 years is about 15 percent IRR, 3x in 5 years is about 25 percent.
• CAGR questions are the same math run in reverse: find the factor, then read the rate off the table you memorized.
• Say the mechanism out loud: "20 percent compounds, so I multiply by 1.2 each year" beats a silent correct answer.

Why does compounding beat addition?

Interviewers set the additive trap on purpose. "Up 20 percent, then up 20 percent" invites 40 percent, and the right answer is 44 percent because the second year's growth applies to the larger base. The one-line fix is to convert every growth rate into a multiplier before touching the numbers: x percent growth means multiply by (1 + x), and n years means multiply n times.

$$\text{Ending value} = \text{Beginning value} \times (1 + g)^n$$

Say the multiplier first, then compute. "1.2 times 1.2 is 1.44, times 1.2 again is about 1.73, so 100 grows to roughly 173" is the answer format an interviewer wants: mechanism, then arithmetic, then a rounded landing.

What factors should be automatic?

The interview range is narrow: growth rates from 5 to 25 percent over 2 to 5 years. That whole range collapses into a short memorized table.

Two patterns do most of the work. Squaring covers the common two-year ask: 1.1² = 1.21, 1.2² = 1.44, 1.25² = 1.56, 1.5² = 2.25. And the 5-year column is the one interviews live in: 15 percent lands on 2.0, 20 percent on 2.5, 25 percent on 3.0. The 15 percent row doubles as the doubling row: 1.15 to the fifth power lands almost exactly on 2, which is the Rule of 72 in disguise.

For a rate outside the table, interpolate between the two nearest rows and say you are approximating. An 18 percent grower over 3 years sits between 1.52 and 1.73, so "about 1.6" is a defensible answer delivered in seconds.

How does the Rule of 72 work?

The Rule of 72 estimates doubling time: divide 72 by the annual rate to get years, or divide 72 by the years to get the required rate. It exists because ln(2) is about 0.693, and 72 is the nearest number that divides cleanly by 2, 3, 4, 6, 8, 9, 12, and 18.

• 12 percent growth doubles in about 72 ÷ 12 = 6 years.
• Doubling in 4 years needs about 72 ÷ 4 = 18 percent a year.
• Tripling has the same shape with 114 in place of 72, but at this range the table is sharper: 3x in 5 years lands on the 25 percent row (3.05), so call it about 24.

The rule runs both directions, which is what makes it interview ammunition: "the fund needs 2.5x in 4 years" becomes "that is one-and-a-third doublings, so doubling every 3 years lands it, 72 ÷ 3 = about a 24 percent IRR" (the true figure is 25.7). That is the exact shortcut behind the return questions in a paper LBO, where IRR and MOIC are the same math wearing two labels.

How do you reverse-solve a CAGR?

A CAGR ask hands you the beginning, the ending, and the years, then wants the rate. Do not reach for the nth root formula out loud. Compute the total factor first, then read the rate off the memorized table.

Worked example: "Revenue went from 80 million dollars to 200 million dollars in 5 years. What CAGR?" The factor is 200 ÷ 80 = 2.5. Scan the 5-year column: 20 percent gives 2.49, so the answer is about 20 percent. The whole solve is one division plus one table lookup.

When the factor lands between rows, bracket it and move on: "2.5 sits between 20 and 25 percent, call it about 20 to 21 percent." Interviewers grade the method and the bracket, not the decimal.

How is this tested under time pressure?

Timed screens and live questions use the same three shapes: forward growth ("what is 90 million dollars after 3 years at 15 percent"), doubling time ("when does this double at 8 percent"), and the reverse CAGR above. The numerical reasoning tests some banks run lean heavily on the forward shape, and the live versions show up inside mental math practice sets alongside margins and multiples.

The failure pattern is always the same: candidates who add instead of multiplying, and candidates who compute silently and lose the interviewer. Convert to a multiplier, narrate each step, land on a rounded answer with the unit attached.

The timed set below runs all three shapes from this article: a Rule of 72 doubling time, a two-year compounding check, and a backwards growth-rate solve. Each question shows the shortcut before you answer.

Quick Math

1. A bank's fee pool grows 8% a year. Using the Rule of 72, how many years does it take to double?

   Rule of 72: years to double = 72 ÷ growth rate.

2. Revenue grows 20% in year one and 20% again in year two. What is the cumulative two-year growth?

   Growth compounds: multiply (1 + rate) by itself, never add the two rates.

3. EBITDA doubled in 4 years. Roughly what annual growth rate does that imply?

   Run the Rule of 72 backwards: rate = 72 ÷ years to double.

Frequently Asked Questions

Is the Rule of 72 exact?

No, it is an approximation that is most accurate between about 6 and 10 percent. At 20 percent it says 3.6 years to double against a true 3.8, which is close enough for any interview answer.

What if the growth rate changes each year?

Multiply each year separately: up 10 then up 20 is 1.1 × 1.2 = 1.32, so 32 percent total. Never average the rates.

How many decimals should I give?

One significant figure past the memorized factor at most. "About 1.7x" or "roughly 20 percent" is the right precision; a third decimal reads as false confidence.

Does this work for declines?

Yes: a 20 percent decline multiplies by 0.8. Two years of 20 percent declines is 0.64, a 36 percent total fall, not 40 percent.

Sources

• Corporate Finance Institute, "Rule of 72": https://corporatefinanceinstitute.com/resources/wealth-management/rule-of-72/ (checked September 2026)
• Wikipedia, "Compound annual growth rate": https://en.wikipedia.org/wiki/Compound_annual_growth_rate (checked September 2026)