What does your savings rate
actually earn after compounding?

Field guide

APR vs. APY: why banks use different numbers for saving and borrowing.

When you deposit money, banks advertise the APY (Annual Percentage Yield). When you borrow, they advertise the APR (Annual Percentage Rate, also called the nominal rate). This asymmetry is not an accident.

APY is always higher than (or equal to) APR for the same underlying rate, because APY accounts for compounding, earning interest on interest that has already been credited. A 5% APR compounded daily yields 5.127% APY. That extra 0.127% sounds trivial, but on a $500,000 savings balance it's $635 of extra income per year without any additional work.

Banks show APY on deposits because it's the larger number; it looks more attractive to savers. They show APR on loans because it's the smaller number; it looks cheaper to borrowers. The Truth in Savings Act (Regulation DD) requires banks to disclose APY on deposit accounts; the Truth in Lending Act (Regulation Z) requires APR disclosure on loans. Both laws protect consumers, but the result is that the same underlying rate looks different depending on which product you're looking at.

The math behind APY.

The formula is:

Where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. The more frequently interest is compounded, the higher the APY, but the gains diminish as frequency increases.

The theoretical limit as n → ∞ is continuous compounding:

For practical rates (1–10%), the difference between daily and continuous compounding is less than 0.001% APY, essentially zero. The meaningful jump in compounding benefit happens between annually and monthly, not between daily and continuous.

How daily compounding works in practice.

A savings account with 5% APR compounded daily doesn't mean you see a deposit every day. What happens:

1. Each day, the bank calculates and accrues interest: daily rate = 5% ÷ 365 = 0.01370% of your balance.
2. That accrued interest is added to your principal; it starts earning interest itself from the next day.
3. At statement periods (monthly or annually), you see the cumulative credited amount. But the compounding is happening every day even if the deposit shows up monthly.

The result after 365 days on $10,000 at 5% APR:

• No compounding (simple): $10,500.00
• Annual compounding: $10,500.00 (same as simple for 1 year)
• Monthly compounding: $10,511.62
• Daily compounding: $10,512.67
• Continuous: $10,512.71

The difference between annual and daily is $12.67 per $10,000 per year , about 0.13%. Over 30 years with regular contributions, this compounds into a meaningfully larger balance.

APY for loans: why it matters when borrowing too.

On the borrowing side, understanding APY helps you compare loan costs accurately. A credit card charging 22% APR compounded daily has an effective APY of 24.36%: meaning you effectively pay 24.36% annually on any balance carried, not 22%. When comparing loan products quoted at different compounding frequencies, always convert to APY (or effective annual rate) for a fair comparison.

Mortgages in the US are typically quoted as APR and compounded monthly, so their APR and effective annual rate are close. Canadian mortgages are compounded semiannually by law, creating a larger gap between the quoted rate and the effective rate.

Where you encounter different compounding frequencies.

Disclaimer

This calculator computes APY from a constant nominal rate and does not model variable-rate accounts, fees, minimum balance requirements, or tax treatment of interest income. Actual yields may differ. Always verify the APY disclosed by your financial institution under Regulation DD.