This is the account: Now concerning the collection for the saints: as I directed the churches of Galatia, so you also are to do. On the first day of every week, each of you is to put something aside and store it up, as he may prosper, so that there will be no collecting when I come.  And when I arrive, I will send those whom you accredit by letter to carry your gift to Jerusalem.  Paul did not want each Corinthian believer to start his gift collection on the day of his arrival.  So he directed each of them to start his gift collection way before his arrival by systematically putting aside something and storing it every Sunday.  Wages were paid in the evening[1] probably at the end of the week and so the prudent time to put aside something and store it would be Sunday, the day straight after receiving the wages, before the wages got expended in the course of the following week. 

Paul was not saying, as some who do not read carefully assume, that since they were holding services every Sunday they should during the service hand over part of their wages for the church to accumulate all the offerings of all believers.  When read carefully, Paul directed each believer to do two things – (a) to put aside part of his own wages, and (b) to store up the part of his own wages he had put aside.  Each believer would not be able to store up for himself his own gift collection if he were to hand it over to the church every Sunday during service.  If they were holding services every Sunday and Paul had intended the church during the services to collect and accumulate all the offerings of all believer, as some suppose, he would have written: “On the first day of every week, as you gather together, each of you is to hand over what you had put aside …”  He did not write as such.

[1] Mt 20.8.