I’m a parent here and my daughter received a BS in Architecture from Washington University in St Louis and a Masters from Washington University. It took her 4 years to get her BS and 2 years to get her Masters. They accepted her into an accelerated track at UW. She had the option to finish her Masters at WashU on a scholarship (very easy acceptance) but wanted to attend a different Arch school. Washu is very design focused and Washington is more technical (different is the point). She was the youngest on her class and is so happy she finished her Masters immediately. Now she is studying for the license exam.
My suggestion is to be careful in enrolling in a five year BArch because of the demands of the curriculum. However that also depends on the school rigor. My daughter found WashU extremely exhausting and it takes over your life. She kept her classes to 16 credits or less. In some cases she only had 12 credits. She had several AP courses which helped lighten her load. She told me many people have dropped out and the class size was halved easily due to the rigor. If you look at BArch they are squeezing all the courses into a 5 year program and that means 18 credits a semester. That would not work at all for my daughter. So it’s important to know what your child can handle.
As far as saving money, there are many ways to do this. One is enroll in a smaller college that offers scholarships and get a degree and Then get a masters in architecture. Another way is get financial aid (if you can get it) at a school like Washu and then get into the masters program (it’s easier if you are already admitted as undergrad); or get a BS in Arch and find a three year program that offers an accelerated track. My daughter saved a year + of tuition going this route.
Honestly I would highly recommend BS in Arch at a well rounded university so if for some reason Arch doesn’t work out your child can easily move into another major. It’s very hard for 15/16/17 year old to know exactly what they want to do with the rest of their life. Also attending a summer Arch program during high school may help too.
Good luck!!