When you reply, please include a clear listing of your work and reasoning so far, so we can "see" where you're having trouble. Thank you!
Assuming this is simple interest, the interest paid each year would be 0.0725(1000)= $72.50. Since the interest paid is less than that, $50.05, the time period must be less than a year: 50.05/72.50= 0.69 of a year. How many days, or months and days is that? "Back off" from Nov. 16, 2007 by that much.
Of course, if this is compound interest, that calculation wrong.
Multiply this by 365 to get the number of days: 252 days. Now work back 252 days from Nov 16 2007. The easiest way of doing this is to use a spreadsheet like Excel; enter the date in one cell, and then in another cell create a formula to subtract 252 from the first cell. Excel will then display the answer as a date. The answer I've got is Mar 9 2007.