A little known fact is the United States Post Office will allow a person to collect mail without renting a P.O Box. There is no application - you'll go into the office and speak to the Postmaster about General Delivery. Of course there are restrictions. For one you will need an ID to collect your mail. Visit the General Delivery webpage for more details and limitations.
If you can afford it, I'd recommend opening a P.O Box over a general delivery. Regardless of how you apply for a p.o box, you should know that the post office will require you to provide proof of a residential address in order to open a post office box. You can fill out an online application here, and pay at the location. If you prefer to- print a paper application here, keeping in mind some locations do not accept paper applications.
Pro tip - If you are able to travel then compare prices of P.O Boxes as they vary by location. You can save money by paying for the year in advance. If you no longer need it - you will get a partial refunding according to the USPS refund policy.
Warning! on permanent forwarding of mail.
With the abundance of services offered by the Post Office you'll have more confidence that your letter arrived on time. Let's imagine you have an housing application deadline - somehow you lost track of time or maybe in the past they 'didn't get' your application at all. In this imaginary situation you can pay for overnight delivery and get your important application in on time (signature included in cost if selected).
You can add additional mailing services, without sending the item overnight. I like that the Post Office is tech savvy and allows it's clients to view the status details online. These services starts at approximately $26, so I challenge you to view their webpage here or speak with your postal clerk about the financial cost and then weigh the benefits of using overnight and other services.
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