A basic formula for restaking

So I see people ask on here occasionally how often they should take interest on staked coins, liquidity pools, et cetera.

So as a PSA for those who are just starting to dip their toes into defi and don’t know, there’s a fairly simple rule of thumb which (while not perfect) can give you a decent idea.

It’s C=m(it)^2

C is the total cost of taking the interest and restaking it (and anything in between, like swap fees).

m is how much you already have invested and earning interest.

i is the annual interest rate without compounding at all (APR).

t is the time period since you last restaked, in years. Yes, it is usually less than 1.

Explanation:

To start, mit is the amount you’ll be recieving when you take your interest – the amount earning the interest, times the interest per year, times the number of years.

Thus (mit)*(it) is the amount of additional interest *on* that interest you’ll have earned by the *next* time you take your interest. And (mit)*(it) is the same as m(it)^2

This means that when C=m(it)^2 , the interest *on* your interest from period 1 will exactly cover the cost of restaking again in period 2. It’s obvious why restaking it sooner than this is a bad idea – if C>m(it)^2 you’ll actually have less money earning interest after two restakes than if you’d skipped the first restaking entirely.

Obviously, as you compound, m will increase. So from time to time you want to recalculate. When you do, you want to calculate using the m from just *before* you last restaked – the mit from your last restake is still paying for itself.

This method isn’t perfect, and it *does* make a couple of assumptions.

The two most relevant assumptions for crypto are that it assumes the cost and interest rate are fixed (for a lot of crypto products they aren’t, but hopefully if you’re using a basic rule of thumb like this you’re not investing in anything *too* unstable), and that it assumes you’ll be restaking at the same interest rate you initially staked at (sometimes your rewards for staking Acoin might be Bthereum, and you might want to stake the Bthereum rather than converting it to Acoin). The first is pretty hard to adjust for, the second is easier, but still makes for a harder to remember formula than C=m(it)^2

(I *think* this is flaired correctly? It might be advice.)

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