“Compounded daily” appears on savings advertisements because it is true, it sounds like an advantage, and almost nobody checks what it is worth.
It is worth about a hundredth of a percentage point.
The arithmetic
More frequent compounding means interest starts earning interest sooner. The annual percentage yield that results is:
APY = (1 + r/n)^n - 1
where r is the nominal annual rate and n is the number of compounding
periods in a year.
At a nominal 5%:
The pattern is the thing to take away: the first step is most of the effect and each one after it is smaller.
Annual to monthly adds about 0.12 percentage points. Monthly to daily adds about 0.01. There is a ceiling, the continuous compounding limit, which at 5% is roughly 5.127%, and daily is already within a thousandth of a point of it. An account compounding hourly would have nothing left to win.
In dollars
On $10,000 held for a year at a 5% nominal rate:
| Compounding | Interest |
|---|---|
| Annually | $500.00 |
| Monthly | $511.62 |
| Daily | $512.67 |
Monthly beats annual by $11.62. Daily beats monthly by $1.05.
Meanwhile a bank offering 5.25% instead of 5.00%, compounded monthly, pays $537.82. That rate difference is worth roughly twenty-five times the daily-versus-monthly upgrade.
What to compare instead
The APY, and nothing else.
APY already contains the compounding frequency by construction. That is the entire point of it, and it is why the Truth in Savings Act requires it: without a single mandated basis, a bank could quote a nominal rate with an unusual frequency and look better than it is.
The calculation is specified in Appendix A to Part 1030. Two APYs are directly comparable no matter how often each account compounds, so once you have both figures the frequency has already been accounted for.
Where frequency does matter
Two cases, both narrow.
When only a nominal rate is quoted. Some comparisons, particularly against non-deposit products, give a nominal rate with no APY. Then you need the frequency to convert, and our APY calculator does it in both directions.
When the balance is very large. A hundredth of a point on $10,000 is a dollar. On $2,000,000 it is $200. Still small against the rate, and no longer nothing.
What this site assumes
Every savings page states its compounding frequency next to the result, because a yield figure with an unstated frequency is not checkable. The default is monthly, which is the most common convention on US deposit accounts, and it is an input you can change.
Every figure is also before tax, and for a taxable account tax takes a far larger bite than any compounding frequency ever will.
Questions
- Does daily compounding beat monthly by much?
- At a 5 percent nominal rate, daily compounding yields 5.1267 percent and monthly yields 5.1162 percent. The difference is about one hundredth of a percentage point, which on a 10,000 dollar balance is roughly one dollar a year.
- Then why do banks advertise it?
- Because it is true, it sounds like a benefit, and it costs them very little to offer. None of that makes it wrong to mention. It just means it should not carry much weight against a rate difference that is twenty times larger.
- What should I compare instead?
- The APY. It already contains the compounding frequency by construction, which is the entire reason Regulation DD requires banks to quote it. Two APYs are directly comparable no matter how often each account compounds.
- Is there a limit to how much compounding can add?
- Yes. As the frequency rises the yield approaches a ceiling, the continuous compounding limit, which at a 5 percent nominal rate is about 5.127 percent. Daily is already within a thousandth of a point of it, so there is nothing left for an hourly account to win.