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He's talking about compounding interest. The difference is so small because you either A) make a few cents each day, and those few cents accumulate by the end of the month to earn SLIGHTLY more interest or B) your interest is issued at the end of the month, and it can help you earn more interest for the next month.
APY (Yearly) vs Rate (monthly):
So APY turns out to be more than the "rate" because they assume you will have money in your account that will accumulate interest, therefore allowing the interest to accumulate interest. In other words, you would make (in pcbanker's case) 6.25% of 100 bucks if you left that in there for the whole year. However, when it comes to the end of the month you only get interest computed by taking 6.06% (for the year), divided by 12 (to make it monthly)
To top it off, here's an explanation that you can't contest:
Let's say you have 100 bucks, and the bank has an APY of 6.25% and a "rate" of 6.06%. Every month, you gain 6.06% of your balance, divided by 12. These are slightly rounded.
Starting balance: $100
Monthly interest is computed by: <the current balance> x 6.06% divided by 12
1st month: gain .505 (giving you a balance of 100.505) (next month's computed interest includes the added interest from current month)
2nd month: gain .50755025 (giving you a balance of 101.01255025)
3rd month: gain .5101133787625 (giving you a balance of 101.522684037625)
4th month: gain .512689451
5th month: gain .51527853
6th month: gain .5178806896
7th month: gain .520495989
8th month: gain .52312449
9th month: gain .52576627
10th month: gain .52842139
11th month: gain .53109022121
12th month: gain .53377192383
Total gain = $6.25
End balance = $106.25
In this example, you are consistently taking 6.06% of the figure and dividing it by 12 to compute the monthly interest, however since the balance increases every month, the amount of interest increases, and the resulting APY (after a year) for this rate is 6.25% APY.