Compounding Math and Shortcuts

Instead of constantly referring to a compounding table, you can use the law of 72 which gives you a rough estimate of how long it takes to double a sum to find your compounding rate.

A price of a painting goes from 250 to 50 million in 100 years. What is the annual rate of return?

Ans: 13%

1. 250 doubles 17.6 times to get to 50 million. 50,000,000 / 250 = 200,000
2. Stated in another way, how many times do you have to double to get from 1 to 200,000?
3. 2^x = 200,000

4.  The base-2 log of 200,000 is about 17.6    x = 17.6
5. 100 years   100/17.6 = 5.7    A double every 5.7 years
6. Use the law of 72      72/5.7 = 12.6% or roughly 13%

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Buffett asks A what he paid for the car. A replies:  "127,500." Buffett immediately: "You could have bought X instead for $45,250. At 12% in Z years that difference would be worth [insert correct answer]


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Also, for mental math, here's a fast trick

99x99 =

1.    99 x 100 = 9,900
2.    9,900 - 99 = 9,801


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Coke

Assume 1.8B 8oz servings of Coke products sold. Assume 1 penny extra, 18 million dollars a day (1/100 x 1800M) .
In one year, how much additional money will coke make if they raise prices by 1 penny?

1. 365 days x 18,000,000 =
2. 365 x 18 =
3. (365 ) x (20 - 2) = (365 x 20) - (365x2) =  7300M - 730M
4. 7.3B - 730M = 7.3 - 0.73 = 6.57B
5. 6.57B or 6 billion and 570 million dollars