Infrarenal aortic aneurism(aneurysm)

My husband recently had a cat scan to diagnose fractured ribs.  This scan also diagnosed a 3.7 cm infrarenal aneurysm. He has cat scans approximately every 6 months due to a liver transplant, so this has appeared in only the last 6 months or so. My question is how fast will this grow and how dangerous is it?  If it burst what will happen? How long will we have to get him to the hospital? We live about 45 miles from the nearest hospital. He also has a stent in his circumflex artery? due to a 90% blockage 4 years ago. Is there any medication to treat this? Could it be causing a drastic rise in his blood pressure such as 189/128, 225/178 pulse rate is never below 115 even in resting position.  What should our next step be? He has an appointment with his heart dr on Nov. 7.

Thanks for your help.

[Cleveland Clinic]

A 3.7 cm aneurysm is not likely to rupture soon, and the most important thing you need to make sure to prevent it from growing is to make sure his blood pressure NEVER gets above 130/80. It is the hypertension which is causing the aneurysm in all likelihood. There are rare instances in which it cuts off blood flow to a kidney and this secondarily causes a rise in blood pressure.
Surgery, in asymptomatic patients with aneurysms of this size is generally not warranted. They also tend to grow slowly if blood pressure is controlled, and require only yearly scans to follow up at this early stage.