Your title asked for a string, but the question text asked for an enumerable. Which is it?
Anyway, here's the enumerable:
public IEnumerable<DateTime> GetPaymentDates()
{
DateTime first = new DateTime(DateTime.Today.Year, DateTime.Today.Month, 1);
DateTime fifteenth = first.AddDays(14);
for (int i=0;i<4;i++)
{
yield return first;
yield return fifteenth;
first = first.AddMonths(1);
fifteenth = first.AddDays(14);
}
}
or a version that returns the strings:
public IEnumerable<string> GetPaymentDates()
{
DateTime current = new DateTime(DateTime.Today.Year, DateTime.Today.Month, 1);
for (int i=0;i<4;i++)
{
yield return current.ToString("MMMM 1st");
yield return current.ToString("MMMM 15th");
current = current.AddMonths(1);
}
}