Formula for growth

Question

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.

Answer 1

For anyone else who is preparing for case interviews, I’ve put together this material that covers virtually all the formulas you need:

Cheatsheet: The Must-Know Consulting Terms for Interviews

Best,

Cristian

Answer 2

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

Answer 3

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

Answer 4

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