How this number is made
The same nominal rate pays more when it compounds more often. This page puts annual compounding next to daily compounding and shows the gap. The gap is real and usually small next to a one-point change in the rate itself. Monthly deposits are not included.
- Use the nominal rate, the one that is not already an APY.
- If the bank already quoted an APY, you do not need this conversion.
Formula
Annual = principal × (1 + rate) ^ years. Daily = principal × (1 + rate ÷ 365) ^ (365 × years).
Worked example
With the figures already in the form, extra from daily compounding is $77.22.
Questions
Is daily the same as continuous?
Almost. Continuous compounding is a hair more and is not what a bank does.
Why is the difference so small?
Because the extra compounding is interest on interest inside the year. The rate you negotiate matters more.