How long does doxycycline stay in your body after you finish your prescribed amount?

It will take approximately 5 days before doxycycline is eliminated from your system

The elimination half life of doxycycline is between 16 to 22 hours (for healthy adults).
This is the time it takes for your body to reduce the plasma levels by half.
It usually takes around 5.5 x elimination half-life (hours) before a drug is completely cleared from your system.
So if we take the maximum elimination half life of 22 hours, it would take 121 hours (5.5 x 22 hours) approximately 5 days before the medicine is eliminated from your system.

Other factors also need to be taken into account and include:
1. How much and how often you have taken the drug.
2. Your metabolic rate – a slower metabolism will increase the time a drug remains in your system.
3. Your age and health – older age and poor health will generally increase the time the drug stays in your system.
4. Body mass – generally the bigger you are the longer a drug will remain in your system.

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https://www.drugs.com/doxycycline.html