Will re-do my post.
I have quite some experience with Migraciones, after many months to get my carnet and their laws, not all of which are apparent until you run up against them(the laws).
Firstly, somewhere back on this site, 2018,there were postings about Americans being limited to 90 days only for tourist visas.....don't know if that is the case or not...anyone else clarify that for this person, please?
Now, if that is not the case, the maximum number of days for a tourist visa is 183 days in any 365 day period...not just a calendar year.
The number of days are calculated from your first visit to Peru, so assuming this is your first visit, then I suggest that you put "visiting friends & relatives" on your immigration card, before you go thru Immigration at the airport.That may help you get the 183 days.
With that marked in the entry stamp in your passport, you may leave and return until the 183 days are used up.
If you stay longer than the 183 days, for example, you stay for the year as you mentioned in your post, then you WILL have to pay a multa(fine) at the airport before you are permitted to leave.
Some people still try "border hopping" to extend their tourist visa...but that's not really safe to do, because it all depends on how alert/diligent the immig' officer is at the airport. You could more than likely find yourself barred from entry.
The rate is US$1.00 per day of overstay. So that's about $180 for your extra 6 months .
I don't know if you can pay in dollars at the airport, or IF it has to be in Soles equivalent.You would need to have the correct amount....getting change could be an issue.
After that, I think that you are are permitted to return to Peru after 6 months...but that needs to be confirmed...could be a year now??!!
Once you have overstayed your 183 day visa, you are classified as illegal, and, if discovered by some random check, you will be forced to leave the country within a few days.
You might like to consider a working visa, IF you could work here.There is info on this, and others, on Migraciones web site.
Hope this helps...any other queries, please ask.