Stable Balance is a Fedi feature that allows you to lock in the fiat value of your bitcoin at the time of deposit. Simply transfer funds from your main Bitcoin Balance to your fiat Stable Balance, and as bitcoin's price fluctuates, so will the amount of bitcoin you hold.
If the price of bitcoin increases, you will have fewer sats; if bitcoin's price decreases, your sats balance will increase to make up for the drop in price. The feature aims to provide peace of mind against bitcoin's price volatility by stabilizing the fiat value of your bitcoin.
To put it simply, if you move 20 USD worth of bitcoin into Stable Balance, you will receive 20 USD worth of bitcoin when you withdraw back to your main balance, though the amount of bitcoin may be more or less than initially deposited depending on bitcoin's price action during that time.
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