Ever wanted to calculate the inflation rate of something quickly? Here’s how!

(Requirements: a calculator with a 1/x button and an x^y button, like the iPhone calculator app in wide mode).

Inputs:

• start price

• final price

• years between

Procedure:

• Enter the final price

• Hit ➗

• Enter the start price

• Hit 🟰

• Hit the “x^y” button

• Enter the years

• Hit the “1/x” button.

• Hit 🟰

At this point, you’re looking at the proportional value for annualized inflation. So 1.25 means +25%, etc.

That’s it! This is a memorizable procedure once you’ve done it a few times.

Example: Suppose a home is listed for $700k, and was last sold for $500k five years ago.

• Enter 7️⃣0️⃣0️⃣0️⃣0️⃣0️⃣

• Hit ➗

• Enter 5️⃣0️⃣0️⃣0️⃣0️⃣0️⃣

• Hit 🟰 (calculator reads 1.4)

• Hit “x^y” button

• Enter 5️⃣

• Hit “1/x” button (calculator reads 0.2)

• Hit 🟰

Final result: 1.069610…

Converted to percentage: +6.96%

So the hypothetical house in question has appreciated at a compound annual growth rate (CAGR) of about 7%. Considering the money supply increases by 8-12% per year, it is underperforming slightly, but still a decent store of value. #math

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Discussion

This is wizardry. I need to learn how to use a calculator 🤣

It’s just some algebra applied to the compound growth formula, and condensed into calculator instructions. 😅

The compound growth formula is:

final = start (1 + rate) ^ n

Where n is the number of periods (years in our case). Given the other values, we can solve for rate:

final = start (1 + rate) ^ n

final / start = (1 + rate) ^ n

( final / start ) ^ (1/n) = ( (1 + rate) ^ n ) ^ (1/n)

( final / start ) ^ (1/n) = (1 + rate)

1 + rate = ( final / start ) ^ (1/n)

Skipped a few steps in the derivation, but you get the idea. So all you have to do is divide final by start, then raise that value to the inverse of the number of periods.

You can use this to compute your gains in fiat terms. For example, if you bought Bitcoin in the crab market of $9k in 2020, then:

(1 + rate) = ( 63k / 9k ) ^ (1/4)

1 + rate = 1.6266…

rate = +63% CAGR

Thanks for this “How to develop depression 101” 😂

I’m here to serve 🕺