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I have bitcoin-qt and was just recently aware that it changes addresses all the time. I am afraid that my last wallet.dat backup was before my last transaction, at which the receiving address was changed.
After that, I had to reinstall my computer. Bitcoin-qt is still 2yrs behind and syncing.
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You're probably safe. If you were using an old version of Bitcoin Core, it used to keep a key pool of 100 unused addresses around. When you request a new receiving address, one from that pool gets used. So, unless you received numerous transactions between the backup and the last transaction, your last transaction should be covered by the backup containing these 100 unused addresses.
If you're using a new version of Bitcoin Core, its wallet uses a hierarchical determistic key derivation where a single backup will always be enough to regenerate any later generated addresses.
Therefore, you should see our transactions appear when your Bitcoin wallet has synchronized with the current state of the network.
I can also confirm that this still works if you have a wallet.dat from 2013 and use the software from 2017. – Ulu83 – 2017-08-16T19:30:59.243
@Ulu83: Yay, glad that it worked out for you. :) – Murch – 2017-08-16T19:46:33.473