Short answer: frequency matters a little, and far less than the rate itself. On $10,000 at 5% for 10 years, the entire spread between annual and daily compounding is about $198. Between monthly and daily, it's about $17.
The exact numbers
$10,000 at a 5% annual rate, held 10 years:
| Compounding | Balance after 10 years | Effective APY |
|---|---|---|
| Annually | $16,288.95 | 5.000% |
| Quarterly | $16,436.19 | 5.095% |
| Monthly | $16,470.09 | 5.116% |
| Daily | $16,486.65 | 5.127% |
| Continuous (theoretical) | $16,487.21 | 5.127% |
Each step toward more frequent compounding earns a smaller bonus than the last. Annual → quarterly gains $147; quarterly → monthly $34; monthly → daily $17; daily → continuous, 56 cents. Compounding frequency has sharply diminishing returns — which banks know when they advertise "daily compounding".
APY already answers this question
The APY (annual percentage yield) on a savings account is the rate aftercompounding is baked in. Two accounts with the same APY pay identically, whatever their stated frequency. So when you're comparing HYSAs, compare APYs and ignore the compounding marketing entirely.
When frequency does matter: debt
Credit cards typically compound daily. On a $8,000 balance at 24% APR, daily compounding produces an effective 27.1% APY — the same diminishing-returns math, but working against you at a rate five times higher than a savings account. Frequency is a rounding error on your savings and a real cost on high-rate debt.