Formula for growth

Question

case math

New answer on Sep 25, 2019

3 Answers

1.1 k Views

Anonymous A asked on Sep 24, 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.

Overview of answers

Sort by:

Only show saved answers

Related Cases

Expert case by Francesco

MBB Final Round Case - Smart Education

Unlock with Premium

Style:

Interviewer-led (McKinsey style)

Topics:

Growth strategy , Market analysis , Market entry , New product

Rating:

4.6

Our client is SmartBridge, a nonprofit educational institution offering face-to-face tutoring services. The client operates in the US.The mission of SmartBridge is to help as many students as possible to complete studies and prevent that they drop from the school system, in particular in disadv ... (Open whole case)

24.6k

Times solved

4.6

600+ Ratings

Advanced

Difficulty

Airline Economics

Unlock with Premium

Style:

Candidate-led (usual style)

Topics:

Market sizing , Profitability analysis

Rating:

4.3

We are an airline major operating out of India. We want to increase the number of passengers on all our flights. Could you please calculate the financial return of adding one more passenger per flight? ... (Open whole case)

16.1k

Times solved

4.3

700+ Ratings

Intermediate

Difficulty

REA Reinsurance

Unlock with Premium

Style:

Interviewer-led (McKinsey style)

Topics:

Mergers & Acquisition

Rating:

4.0

Your client, REA, is a reinsurance company.REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA.However, the acquisition is not well recei ... (Open whole case)

11.6k

Times solved

4.0

900+ Ratings

Advanced

Difficulty

Expert case by Francesco

Bain 1st Round Case – BlissOttica

Unlock with Premium

Style:

Candidate-led (usual style)

Topics:

Growth strategy , Market analysis , Market entry , Profitability analysis

Rating:

4.2

Our client is a BlissOttica, an Eyewear Manufacturer that is looking to reach a 10% increase in profits. How would you help our client? ... (Open whole case)

8.8k

Times solved

4.2

100+ Ratings

Intermediate

Difficulty

Expert case by Ian

Cutting Carbs - Divestiture in the Electrical Power Market

Unlock with Premium

Style:

Candidate-led (usual style)

Topics:

Growth strategy , Mergers & Acquisition , Operations strategy , Valuation

Rating:

4.0

Our client is Energy England, one of northern England’s largest electric utility companies. They were created over the past decade through an aggressive series of mergers of existing utility companies each specializing in a single energy generation source.Recently, the CEO has embarked on an initiat ... (Open whole case)

4.7k

Times solved

4.0

< 100 Ratings

Intermediate

Difficulty

Answer 1

Best answer

Vlad

Expert

Content Creator

replied on Sep 24, 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

Was this answer helpful?

2

Anonymous B on Sep 24, 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?

Answer 2

Aws

Expert

updated an answer on Sep 24, 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

(edited)

Was this answer helpful?

1

Anonymous A on Sep 24, 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...

Anonymous C on Sep 25, 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

Answer 3

Francesco

Expert

Content Creator

replied on Sep 25, 2019

#1 Coach for Sessions (4.000+) | 1.400+ 5-Star Reviews | Proven Success (➡ InterviewOffers.com) | Ex BCG | 9Y+ Coaching

Hi Anonymous,

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

From the rule of 72, the number of years you need to double with a 5% growth rate is approximately 72/5 = 14
This means that in approximately 14 years you will reach 27.6T (13.8*2)
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
Therefore your final proxy is 27.6-5.6 = 22T

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

Best,

Francesco

Was this answer helpful?

0

Formula for growth

Overview of answers

Related Products

Related Cases

Related Bootcamp Articles

Similar Questions

Division Hard

Common Math Mistakes

Case Math

Related Products

5 sessions package with Vlad

Similar Questions

Division Hard

Common Math Mistakes

Case Math