I'm on Mavericks (10.9.5). I have an external USB drive that I use exclusively for Time Machine backups.

I just realized that the backups are unencrypted. Is there a way to configure Time Machine to encrypt all backups on this drive, both existing backups and future backups, without erasing the existing backups?

This answer indicates that it can be done with "sparsebundles", but the post is 5 years old and it seems risky.

Is there an easier way?

Update: I was mistaken that the backups were unencrypted -- they are actually encrypted. I was fooled because Time Machine preference window includes the word "encrypted" below the listed backup disks, but only if the backup disk is plugged in. If the backup disk is not plugged in, Time Machine still lists the backup drive, but it loses the label "encrypted". Doh! In Disk Utility, I verified that the disk is encrypted with FileVault2; moreover, OS X prompts me for a password when I plug in the disk. Would still like to know the answer to my original question though.