What is an easy way to calculate (1.04)^54?

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What is an easy way to calculate (1.04)^54?

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You need to know how to work with exponentials.

1^(a*b) = 1^a^b

1.04^54 = (1.04^9)^6 = ~1.4^6 = (~1.4^2)^3 = ~2^3 = 8

But… why do you ask? Howcome this is necessary in a case interview?

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Hi Cheryl,

Literally a waste of time to figure this out! This will **not** be in a case and this is definitely not what's expected in mental math! (Checkout the Preploung mental math exercises for a better idea…though even some of their advanced/hard ones are still too much!)

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I disagree. They are likely testing if you know the rule of 72. At a 4% growth rate, an investment should double every 18 years. So over the span of 54 years, the investment should 8x (at a 4% growth rate).

I disagree with you Anonymous A. You may see it in a casebook, but it would be complete absurd to ask this in a real consulting interview. Knowing math and arithmetics is a criteria to get into consulting. Knowing financial heuristics (e.g. the rule of 72) is not. May be a nice question for investment banking. Never for consulting.

Such specific questions are actually easier than they look - another method to solve this would be using the 72-rule

72 divided by % growth rate give you the time to double in years

Here, you are working with **1.04** which is nothing but 1 + 4%. So the question can be assumed as a **4% growth rate fund** for **54 years**

72 divided by 4% = 18 years

so in 54 years the money will double 3 times

After 18 years 1 will become 2 growing at 4%

After 36 years it will become 4

After 54 years it will become 8

(edited)

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It is a question from the case, Gravestone Inc.

You are not expected to know how to do this type of mental calculation in an interview, so don't worry about it. You not expected to know financial heuristics.