My mother was a high school mathematics teacher and understood that kids learn best when learning is fun, so at a very young age she started teaching me math “tricks.” In the second grade she showed me how 9 times any number less than 10 was simply that number minus 1 concatenated with the sum of difference plus whatever it takes to get back to 9. For example, 9 x 8 is 8 minus 1 (7) concatenated with 9 minus 7 (2) — 72. I was hooked.
Since then I have been fascinated with finding quick and dirty tricks to arrive at answers (or good approximations) to everything from the probability that my beloved Arizona Wildcats basketball team will win a game to market sizes and rates of return. Below are three of my favorite business hacks.
1. Using “Mathemagic” to Do Rapid Mental Calculations
Being able to rapidly do math in your head will allow you to think about things in real time that can change the course of the discussion. It isn’t that hard to do back-of-the-envelope calculations that give you an idea of the reasonableness of key assumptions with the help of a little mathemagic. For more detail on this, check out Arthur Benjamin’s book “Secrets of Mental Math” or the embedded video below.
In the meantime, here are a few of my favorite tricks.
Square any 2 digit number ending in 5.
For example, let’s square 25.
Step 1: Take the first digit and multiply it by itself plus 1. So 2 x 3 = 6.
Step 2: Take the product from Step 1 and concatenate it with 25 on the right to get 625.
Let’s try again. Square 65.
Step 1: 6 x (6+1) = 42.
Step 2: Append 25 to the right of 42 and you get 4225.
Multiply any two digit number by 11.
For example, let’s multiply 78 x 11.
Step 1: Take the number being multiplied by 11 and add the digits together. So 7 + 8 = 15.
Step 2: Insert a zero between the same two digits. 708.
Step 3: Add the result from Step 1 to the zero of Step 2. In this case we have 15, so we need to carry the 1. An easy way to think about it is 70 + 15 = 85 with the 8 from 708 added at the end for 858.
2. The Rule of 72 (or 69.3 or 70)
If you invest in the stock market and expect your money to earn a return of 5 percent per year, how long will it take for your money to double? If a VC is managing $100 million and limited partners expect a 25 percent annual return, how often do they need to double their money?
The Rule of 72 is a linear approximation — one of the coolest applications of derivatives for the pragmatic businessman. Here is a simple derivation for those of you who care. For everyone else, simply divide the expected (compounding) return into 69, 70 or 72 to find the number of periods it takes to double. So it will take us roughly 14 years to double our money at a 5 percent expected annual return and the VC will need to double his fund every three years or so in order to hit the target return of his limited partners.
Understand that this is an approximation and varies with the size of the return — see the table below from Wikipedia to get a better idea of the precision of the approximation.
3. Solving Problems With Microsoft Excel’s Goal Seek
Goal Seek is the ultimate business hack. When you know the desired result of a formula, but you don’t know the input value the formula requires to yield the result, Goal Seek can help you get your answer. For example, let’s say that you want to figure out the required annual return it takes to double a $100 million fund over three years.
Step 1: Setup the problem.
Step 2: Use goal seek (Tools -> Goal Seek).
“Set cell” = the value you want set, here the value of the fund in Period 3. “To value” = the value you want the cell to be changed to, here we want $100 million x 2 or $200 million. And “By changing cell” = the thing you are trying to determine, here the annual expected rate of return. Hit “OK.”
Step 3. Profit! We need a 26 percent annual return to double every three years. Of course, we could have used the Rule of 72 and a little mathemagic to arrive at this answer without Excel. But Goal Seek works in all types of scenarios.
Hopefully you will find one, or several, of these hacks useful in your job or life. If nothing else, you can use them to impress your friends or to inspire your children.
Mike Speiser is a Managing Director at Sutter Hill Ventures. His thoughts on technology, economics and entrepreneurship will appear at this time every week.