The only reason that the principal balance will affect your APY is rounding. Lower balances (and therefore lower amounts of calculated interest) will cause some weird APY results. You will see them, for example, in the APYE disclosures for two identical, no activity accounts, one with a $2 balance and the other with a $2000 balance (assuming they both earn the same Interest Rate).
Somewhere in the calculation, the APY Checker is rounding a result to a small number of decimals. I assume (there's that word again!) that the interest amount is where it happens.
Example, $2 at 1.25% interest rate for one year yields interest of $0.02 or $0.03 depending on how you round or truncate. $2000 at the same rate yields $25 even. Since the dollar amount of interest gets carried into the APY formula, a lot can depend on whether you use 2 cents or 3 cents. One will get an APY a lot smaller than the interest rate; the other will get one that's a lot larger.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8