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Compound Annual Growth Rate McKinsey PST Questions



How would you approach those two excersises below? I am preparing alone (without a tutor and math/ GMAT prep. background) so I found those tasks rather difficult for me..

I've found suggestion here: https://www.preplounge.com/en/consulting-forum/math-prep-cagr-without-excel-any-tips-750#a1460 to use Taylor series - but that approach seems not to be applicable for all the cases (i.e. if the (1+x)^a=V is (1+(-x))^a - decreasing by 1 p.p. is not helpful at all)..

I am looking for several generic&fast approaches to cover all possible cases (i.e. solutions are too close to each other, growth rate is negative, etc.)

1. The Revenue in Y0 = 11.64. We project annual growth to be 7%. Which of the foll. is the closest estimate of the projected Revenue in Y5?

  • a) 15.2
  • b) 16.3
  • c) 17.4
  • d) 18.5

My approach:

1) 11.64(1+0.07)^5 = y

then either:

2) use binomial formula: (1+x)^5 = 1+5x+10x^2+10x^3+5x^4+x^5 => x = 1.403


3) (1+0.07)^5 = 1.07^4 * 1.07 = 1.15*1.15*1.07=1.323*1.07 = 1.42

4) y = 11.64*1.4 = 16.3 => b)

2. Number of cows 3 years ago - 2 150 000, now - 500 000. Assuming cows declining at a constant rate, which of the foll. is the closest estimate of the annual % drop in the number?

  • a) 20%
  • b) 25%
  • c) 40%
  • d) 55%

My approach:

1) 2 150 000 (1-x)^3 = 500 000

(1-x)^3 = 0.232

2) x=20%:

0.8^3 = 0.64*0.8 = 0.512 => wrong

3) x=25%: too close to 20% => wrong

4) x=40%:

0.6^3 = 0.36*0.6 = 0.216 ~ 0.232

5) x = 55%:

0.45^3 = 0.20*0.45 = 0.09 => wrong.

6) c)

Thank you in advance!

Levente replied on 12/30/2017


whenever you are required to solve a compound interest problem you can go with two different logic:

1. When you want to know how much will value X will be in Y years given Z% growth each year:

1.1. Logic: You should multiply Y with Z that will be the simple growth and then add a compound margin of around 5-10%points (but only in case that Y*Z is small, ie. less or equal 45).

1.2. Example: What will be 100 in 5 years given 7% growth each year. 5*7=35 and then I would add around 5-7%, thus 40-42%. Therefore, around 140-142. The exact answer is 140.25.

2. When you want to know in how many years will be X double given its growth rate of Y%.

2.1. Logic: Rule of 72 says that you should divide 72 by the growth factor which would result the number of years the original value would double.

2.2. Example: In what years will 100 double given its 7% growth each year. 72/7 ~ 10. Little more than 10 years. Exact result: in 10th yearend it will be 196.7, in 11th yearend it will be 210.5. Thus little more than 10 years.

2.3. Additionally, there are even more than this one rule, go to a videostreaming platform and search for Flessibilita. He has a 15 minutes of video on compound margin.



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