Why don't banks calculate interest in CD using continuous compounding (which is higher than compounding quarterly)? While in the case of a mortgage they use continuous compounding.
Most banks calculate mortgage interest monthly. No benefit to paying weeks early each month, and no extra interest paying right up to the day before the late fee kicks in, usually on the 15th day of the cycle. A CD can go either way, but what's most important is what you get at maturity.
Different banks compute interest differently. I wouldn't concern myself with it much --- it doesn't really matter.
Don't know what you're talking about. Just checked the Wells Fargo web site - they compound the CD interest daily.
Differences are entirely due to convention, and conventions may differ between banks or even between products at the same bank. This is why the "APR" exists, with a precise legal definition allowing one to compare rates. The equivalent continuously compounded rate can easily be found for any discretely compounding rate, and vice versa.