It is really helpful to have a wired meat thermometer so you can see when the roast reaches 140 and remove from oven, but this method has worked for me without a problem without a wired one. Also, cooking time may need to be adjusted based on your ovens ability to retain heat.
seasonings as desired
Season the tenderloin to your taste - can marinate for an hour or up to a day.
Place in shallow roasting pan lined with foil. Preheat oven to 550. Calculate cooking time at EXACTLY 5 1/2 minutes per pound. Place meat in oven and cook. When the calculated time is over, turn off oven and set timer for 1 hour. DO NOT OPEN THE OVEN. Allow the heat to cook the roast.
When hour is complete, remove and temp should be about 140. Allow meat to rest for 5 minutes for juices to redistribute. After resting, temp should be around 145-150. Meat will be incredibly tender and juicy.
***You can also add 1 in cut carrots/potatoes to the roasting pan around the loin, but not touching it. Just drizzle with oil and season to taste. Veggies should be cooked perfectly. *watch for an oil that has a very high smoke point. Cooking at this high of temperature can cause oil to smoke*