Put $10,000 in a high-yield savings account at a 4.00% stated rate, let it compound daily, and a year later you'd have about $408.08 in interest. That works out to an APY of 4.08%. The gap between 4.00% and 4.08% is the entire APY vs APR question: one number counts compounding, the other doesn't.
The 4.00% is our illustration, not a rate any particular bank is quoting. We picked it because the math is easy to check. For scale, the FDIC's national average savings rate was 0.37% as of September 21, 2026 — about $37 a year on the same $10,000.
Below, we run one deposit through three compounding schedules, walk through the federal formula behind every APY you see, and then take federal income tax out so the number matches what you actually keep.
Interest earned on $10,000 in one year, illustrative 4.00% rate vs. the 0.37% national average. AI-generated image
$10,000 at 4.00%: simple vs monthly vs daily compounding
A $10,000 deposit at a 4.00% stated rate earns $400.00 in one year with simple interest, $407.42 with monthly compounding, and $408.08 with daily compounding. The extra $8 comes from interest earning interest; the step from monthly to daily is worth only $0.66 at this rate.
| Compounding | Credits per year | Interest after 1 year | APY |
|---|---|---|---|
| Simple (paid once, at year-end) | 1 | $400.00 | 4.00% |
| Monthly | 12 | $407.42 | 4.07% |
| Daily | 365 | $408.08 | 4.08% |
Illustrative 4.00% stated rate, 365-day year, no deposits or withdrawals. Calculations by The Daily Sift.
The mechanics are plain arithmetic. Each period, the bank takes the balance, multiplies it by the rate divided by the number of periods, and adds the result to the balance. With monthly compounding, month one pays $10,000 × (0.04 ÷ 12), or $33.33. Month two pays on $10,033.33. Daily compounding does the same thing in smaller slices — about $1.10 on day one — but 365 times.
That's where the 4.07% and 4.08% come from:
- Monthly: (1 + 0.04/12)^12 − 1 = 4.0742%
- Daily: (1 + 0.04/365)^365 − 1 = 4.0808%
Our read: the compounding schedule is close to a rounding error next to the rate itself. Going from monthly to daily adds $0.66 a year. Going from a 0.37% account to a 4.00% one adds roughly $371. The lower the rate, the smaller the compounding gap gets.
What is the difference between APY and APR on a savings account?
APY (annual percentage yield) is the yearly return after compounding is counted. APR (annual percentage rate) is the stated rate before compounding. When interest compounds more than once a year, the APY on a savings account comes out higher than the stated rate — at 4.00% compounded daily, the APY is 4.08%.
Most people meet APR on credit cards and loans, where it describes what borrowing costs. On a deposit account, the stated rate plays that APR role, and it leaves out the bonus you get from interest landing on top of interest.
APY fixes that. Because it folds compounding in and puts every account on a 365-day footing, it's the number that lets two accounts be compared side by side. Two banks that both say "4.00%" can pay different amounts if one compounds daily and the other once a year. Two banks that both show 4.08% APY pay the same on a steady balance, give or take a cent of rounding.
Bank education pages, PNC's among them, describe APY as the figure deposit advertising has to show under the Truth in Savings Act. We could not confirm that advertising requirement on the CFPB's own page, so we'll stick to what the regulation's formula appendix says directly.
How banks calculate APY under federal rules
Regulation DD's Appendix A gives banks one APY formula: APY = 100 × [(1 + Interest/Principal)^(365/Days in term) − 1]. Interest is the dollars earned over the term, Principal is the amount deposited, and Days in term is the actual number of days. The formula converts any term into a 365-day yearly yield.
Run our daily-compounding example through it. Interest is $408.08, principal is $10,000, and the term is 365 days, so the exponent is 1:
100 × [(1 + 408.08/10,000)^1 − 1] = 100 × 0.040808 = 4.08%
The exponent is the part that does the quiet work. For a term shorter than a year, 365 ÷ Days is bigger than 1, which stretches the short-term return out to a full year. That's why a 90-day promotional account and a 12-month account can still sit on the same APY scale.
One wrinkle: in a leap year, Appendix A lets a bank use either 365 or 366 days. Across a full year, that choice nudges the decimal places, not the dollars.
The federal APY formula applied to $408.08 of interest on $10,000 over 365 days. AI-generated image
What $10,000 keeps after taxes and averages
Savings interest is taxable income, so the $408.08 in our daily-compounding example is not what you keep. Assuming a 22% federal bracket, about $89.78 goes to federal income tax and $318.30 stays. Banks send Form 1099-INT once interest reaches $10, and smaller amounts are still reportable, according to IRS Topic No. 403.
| Federal bracket (assumed) | Federal tax on $408.08 | Interest kept |
|---|---|---|
| 12% | $48.97 | $359.11 |
| 22% | $89.78 | $318.30 |
| 24% | $97.94 | $310.14 |
Approximate; state and local income taxes not included.
Tax also shrinks the compounding edge. At 22%, simple interest leaves $312.00 and monthly compounding leaves $317.79. Daily compounding's after-tax lead over monthly is $0.51 for the year.
The averages put the 4.00% example in context. The FDIC lists the national average at 0.37% for savings and 0.63% for money market accounts, both as of September 21, 2026. On $10,000, those come to roughly $37 and $63 a year before tax. The IRS treats interest from savings, money market accounts, and CDs the same way: it's all taxable.
Safety doesn't change with the rate. FDIC deposit insurance covers up to $250,000 per depositor, per insured bank, for each account ownership category, so a $10,000 balance at an insured bank sits well inside the limit.
At a glance
- The number to compare: APY, because it includes compounding. The stated rate (the APR-style figure) leaves it out.
- How much compounding adds: at 4.00% on $10,000, $408.08 daily versus $400.00 simple — and just $0.66 between daily and monthly.
- The bigger lever: the rate. 4.00% versus the 0.37% national average is about $371 a year.
- The catch: interest is taxable, so in a 22% bracket $408.08 becomes $318.30.
Related on The Daily Sift: CD Rates vs Treasury Yields: What 2026 Savers Get Now · 10-Year Treasury at 5.04%: What It Does to Your Mortgage
Sources
- 12 CFR Part 1030, Appendix A — Annual Percentage Yield Calculation (Cornell LII)
- FDIC — National Rates and Rate Caps
- FDIC — Understanding Deposit Insurance
- IRS — Topic No. 403, Interest Received
This article is for general information about savings account interest, APY, and APR only and is not investment, financial, or tax advice. Figures such as rates, returns, and rules are as of October 6, 2026 and may change. Any financial decision is your own responsibility; please verify with official sources or a licensed professional before acting.