“Interest compounded daily” is one of the most reliable phrases in savings marketing. It sounds like free money — the same rate, working harder, more often.
It is real. It is also, at realistic rates, worth a fraction of what the emphasis implies.
What frequency is actually worth
Take $10,000 at a nominal 6% for thirty years, and vary only how often interest is credited.
| Compounding | Effective annual rate | Balance after 30 years |
|---|---|---|
| Annually | 6.00% | $57,435 |
| Semi-annually | 6.09% | $58,916 |
| Quarterly | 6.14% | $59,693 |
| Monthly | 6.17% | $60,226 |
| Daily | 6.18% | $60,488 |
Thirty years of daily compounding instead of annual is worth $3,053, or about 5.3%. Worth having, and worth choosing when everything else is equal. Not worth accepting a lower headline rate for — a competitor offering 6.1% compounded annually beats 6% compounded daily comfortably.
The reason the gains taper is visible in the middle column. Going from annual to semi-annual buys nine basis points. Monthly to daily buys one. The mathematical limit — continuous compounding, Pert — would give 6.1837%, so daily has already captured essentially all of it.
Compare accounts on effective annual rate, never on nominal rate plus a compounding adjective. EAR already contains the frequency.
The variable that actually matters
Hold the same $10,000 at 6% compounded annually — the worst frequency in the table — and add $100 a month.
| Scenario | Balance after 30 years | Difference |
|---|---|---|
| $10,000, annual compounding | $57,435 | — |
| $10,000, daily compounding | $60,488 | +$3,053 |
| $10,000 + $100/month, annual compounding | $155,361 | +$97,926 |
A hundred dollars a month, at the least favourable compounding schedule in the table, adds $97,926 — about thirty-two times what the frequency upgrade delivered.
This is the ordinary shape of savings arithmetic. Contributions dominate rate, and rate dominates frequency, and the gaps between those tiers are much larger than the marketing emphasis suggests. Frequency is the smallest of the three levers and gets the loudest billing because it is the one costing the bank least.
Where frequency does matter
Three cases where it is worth attention rather than a shrug.
On debt. The same arithmetic runs in reverse and the rates are far higher. A credit card at 22% compounded monthly has an effective rate near 24.4%, and that gap is money leaving your account. See how credit card interest compounds against a fixed payment.
At high rates. The frequency effect scales with the rate. At 6% the annual-to-daily gap is 18 basis points; at 20% it is over 140.
When comparing quoted rates. A product quoting a nominal rate with frequent compounding and one quoting EAR are not directly comparable until you convert. That is exactly what EAR is for, and why regulators in most markets require it.
The rule of 72, and where it breaks
Divide 72 by the rate to approximate the doubling time: 72 ÷ 6 = 12 years. The exact answer at 6% compounded annually is 11.90 years, so the shortcut is good to about a month over a decade.
It degrades at extremes. At 1% the rule says 72 years against a true 69.7; at 25% it says 2.88 against a true 3.11. Fine for a mental estimate in the single-digit range, not for planning.
What to do with this
Compare on effective annual rate. Take the better frequency when the rate is equal. Then stop optimising it, because the next hour is better spent on the contribution line — that is where the 32× lives.