Brainteasers

Mental math for the interview

6 min read · updated July 2, 2026

You will not get a calculator. Someone will slide a number across the table, ask you to double it, take a percent of it, or turn a 3x return over five years into a rate, and they will watch your face while you do it. The math is never the hard part. Your composure is. A banker who freezes on "what's 15% of 80" is telling the room they can't be trusted with a live deal at 11pm.

So train the reflexes. Not the theory, the reflexes. Here's the toolkit.

The rule of 72

This is the one shortcut you must own cold. To find how many years it takes something to double, divide 72 by the growth rate.

$\text{Years to double} \approx \frac{72}{\text{rate }(\%)}$

Money growing at 8% doubles in 9 years. At 12%, in 6 years. At 6%, in 12 years. It runs backwards too: if something doubled in 4 years, the rate was roughly 72 / 4 = 18%.

Key insight

The rule of 72 is really a shortcut for compounding, and compounding is the engine under every return question in finance. If you can double and halve fast, you can approximate almost any growth or discount problem in your head.

Percentages, the fast way

Beginners reach for long multiplication. Don't. Break the percent into pieces you already know.

10% is just move the decimal. 10% of 340 is 34.
5% is half of that. So 5% of 340 is 17.
1% is move the decimal twice. 1% of 340 is 3.4.

Now build any percent from those blocks. 15% of 340? That's 10% (34) plus 5% (17), so 51. 20% of 85? Double the 10%, so 17. This beats grinding every time, and it almost never goes wrong.

Reverse it when you need a margin. A company does 500 of revenue and 75 of operating profit. Margin is 75 / 500. Scale both to 15 / 100. That's 15%. Done in two seconds.

Growth and multiplication with clean numbers

Interviewers pick round numbers on purpose. If a problem feels like it needs a calculator, you probably misread it. Look for the clean version.

Say revenue is 200 and grows 15% a year. Year one adds 30 (that's 15% of 200), so you're at 230. Don't compound in your head past a year or two; nobody expects it, and the interviewer will usually say "assume it stays flat" or "just approximate."

Multiplying by clean multiples is the same idea. A business with 40 of EBITDA at a 6x multiple is worth 240. Take it to a 7x and you've added one turn, another 40, so 280. Thinking in "turns" instead of raw products keeps LBO and valuation math trivial.

Common mistake

Freezing on the arithmetic. The problem was built to work with round numbers, and the interviewer is not testing your long division. When you feel the panic, stop and reach for a shortcut: split the percent into 10s and 1s, use the rule of 72, or round to the nearest clean figure and adjust. Grinding a messy calculation on paper while the room waits is the exact thing they're screening out.

Estimating IRR from MOIC

This trips up almost everyone because they think there's a formula to compute in their head. There isn't, and nobody expects one. You estimate.

MOIC is how many times you got your money back. IRR is the annualized rate that gets you there. The link is just compounding, so the rule of 72 gets you close, and a few memorized anchors get you the rest.

Start from doubling. A 2x over some years means the rule of 72 divided by the years gives the IRR. 2x in 5 years? 72 / 5, roughly 15%. 2x in 3 years? About 24%. 2x in 7 years? About 10%.

For non-double multiples, lean on these anchors. They come up constantly, so memorize them:

| MOIC | Hold period | Approx. IRR | | --- | --- | --- | | 2x | 5 years | ~15% | | 3x | 5 years | ~25% | | 2x | 3 years | ~26% | | 3x | 3 years | ~44% | | 2.5x | 5 years | ~20% |

The pattern to internalize: over a five-year hold, a 2x is mid-teens, a 2.5x is about 20%, and a 3x is mid-20s. If you know those three, you can interpolate anything a paper LBO throws at you. (See the paper LBO for where these numbers actually get used.)

Sanity-check everything

Speed is worthless if the answer is absurd. Before you say a number out loud, ask whether it passes a gut test. A sponsor buying at 8x and selling at 8x with modest debt paydown should land somewhere around a 2x to 2.5x over five years, not a 6x. An IRR above 40% on a boring business should make you suspicious you dropped a zero.

Interview tip

Narrate as you go. "10% of 80 is 8, so 15% is 12" out loud is worth more than a silent correct answer, because it shows the interviewer your process is clean and repeatable. And if you fumble a step, just say "let me redo that" and restate the assumption. Recovering calmly reads as confidence. Freezing reads as someone who'll seize up on a live deal.

How to practice

Do it in the shower, on the walk to class, waiting for coffee. Take any two-digit numbers and find 15% of them. Pick a growth rate and count doublings. Turn a MOIC into an IRR and check it against the table above.

This is trainable, and it's the cheapest edge you can build before a Superday. Everyone studies the accretion/dilution logic and the DCF steps. Fewer people can actually run the numbers fast under pressure, and that gap is exactly where you separate yourself.

Interview tip

The real test isn't a single calculation, it's stringing them together fast: entry multiple to purchase price, purchase price to equity check, EBITDA growth to exit value, exit to MOIC, MOIC to IRR, all in one clean spoken sequence. Drill the whole chain until it flows without hesitation. That fluency, more than any one trick, is what tells a banker you can already do the job.

Glossary

New to the lingo? Every term used above, in plain English.

MOIC (Multiple on Invested Capital): How many times an investor got their money back, calculated as cash returned divided by cash invested. A 2.5x MOIC means getting back 2.5 dollars for every dollar put in. It ignores time.
IRR (Internal Rate of Return): The annualized percentage return on an investment, which accounts for how long the money was tied up. Private equity firms often target an IRR of around 20%.
EBITDA: Earnings Before Interest, Taxes, Depreciation, and Amortization. A rough proxy for a company’s operating cash profit, before financing and accounting choices.
LBO (Leveraged Buyout): Buying a company using mostly borrowed money, then using the company’s own cash flow to pay that debt down over time. The classic private equity playbook.
Multiple: Valuation shorthand like EV/EBITDA or P/E. It shows how many times a metric the market is paying for a company, which lets you compare businesses of different sizes.

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