Formula for growth

case math
Neue Antwort am 25. Sept. 2019
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Anonym A fragte am 24. Sept. 2019

Hello all,

Could you please tell me what is the formula you use to calculate the end number for growth? For example, I know that something that is 13.8 trillion will grow by 5% each year over next 10 years. What is the result in the 10 years? I am sure this is quite simply done, but I don't know how other than doing the 13.8+5% of 13.8 in year one, etc. which I know is not the right way...(time-wise).

I know how to calculate how much something is growing when I have the starting number and the end and what I need to find out is the growth/decline percentage...

Thank you,

A.

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Vlad
Experte
antwortete am 24. Sept. 2019
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

It's the rule of 72:

1) 72 or 70 (whichever is easier to calculate) is devided by 5. Thus 70 / 5 = 14. It's the number of years it takes to double the investment

2) If you have 10 years, then your investment will not double but roughly grow by 1.5-1.7 times

Best

Best

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Anonym B am 24. Sept. 2019

Vlad, can you please explain this rule of 72 and how it relates to the question above with 13.8 trillion with growth of 5% for 10 years?

Aws
Experte
bearbeitete eine Antwort am 24. Sept. 2019
Senior Consultant @ Google | McKinsey, BCG, Bain exp. as Client | 100+ REAL MBB cases

Hi A,

In case interviews you can use a simplistic approach to say:

5% per year x 10 years = 50% growth

Meaning the 13.8 Trillion will be 20.7 Trillion in 10 years. The actual answer is 22.5 Trillion.

With this method I would advise you to round up your numbers and tell the interviewer you know this is an approximation.

Hope this helps.

Best,
Aws

(editiert)

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Anonym A am 24. Sept. 2019

Hi Aws, thank you for your help. This is how I would do it too, but this is not a case question, it is a PST question and I need to get to the 22.5 trillion exactly...

Anonym C am 25. Sept. 2019

No, you don't need to get to the number exactly. You need to be able to approximate. There is no "magic way" to get to this precisely without doing a full compounding calculation

Francesco
Experte
Content Creator
antwortete am 25. Sept. 2019
#1 Coach for Sessions (4.000+) | 1.500+ 5-Star Reviews | Proven Success (➡ InterviewOffers.com) | Ex BCG | 10Y+ Coaching

Hi Anonymous,

you can estimate the result applying the rule of 72 as follows:

  1. From the rule of 72, the number of years you need to double with a 5% growth rate is approximately 72/5 = 14
  2. This means that in approximately 14 years you will reach 27.6T (13.8*2)
  3. Since you are interested in 10 years, you can estimate that decreasing 27.6T by 5% for 4 years, or 5%*27.6*4 = 1.4*4 = 5.6
  4. Therefore your final proxy is 27.6-5.6 = 22T

The exact number is 22.5T, thus pretty close to the estimate.

Best,

Francesco

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Vlad

McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School
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