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# Formula for growth

case math
New answer on Apr 30, 2024
1.6 k Views

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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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

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?

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)

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...

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

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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