401(k) Loan Calculator
Calculate 401(k) loan repayment, interest paid back to yourself, and the opportunity cost of lost market returns. See the true cost of borrowing from retirement.
APY Calculator
Calculate Annual Percentage Yield (APY) from nominal interest rate and compounding frequency. Compare savings growth across compounding periods.
%
$
$
yrs
APY (Annual Percentage Yield)⧉
5.12%
Effective annual return with compounding
Nominal Rate⧉
5.00%
Stated rate before compounding
APY − Nominal Difference⧉
+0.12%
Gain from compounding
Final Balance⧉
$26,491.48
After 5 years
Total Deposits⧉
$22,000.00
Initial + monthly additions
Total Interest Earned⧉
$4,491.48
Growth from compounding
Growth Breakdown
Deposits 83.0%
Interest 17.0%
Compounding Frequency Comparison
| Frequency | APY | Interest on $10,000.00 / yr |
|---|---|---|
| Annually | 5.00% | $2,500.00 |
| Semi-annually | 5.06% | $2,531.25 |
| Quarterly | 5.09% | $2,547.27 |
| Monthly | 5.12% | $2,558.09 |
| Daily | 5.13% | $2,563.37 |
| Continuous | 5.13% | $2,563.55 |
Year-by-Year Growth
| Year | Start Balance | Deposits | Interest | End Balance |
|---|---|---|---|---|
| 1 | $10,000.00 | $2,400.00 | $577.62 | $12,977.62 |
| 2 | $12,977.62 | $2,400.00 | $729.96 | $16,107.59 |
| 3 | $16,107.59 | $2,400.00 | $890.10 | $19,397.68 |
| 4 | $19,397.68 | $2,400.00 | $1,058.43 | $22,856.11 |
| 5 | $22,856.11 | $2,400.00 | $1,235.37 | $26,491.48 |
Planning notes, formulas, and examples
About the APY Calculator
Annual Percentage Yield (APY) represents the real rate of return you earn on savings or investments when compounding is taken into account. Unlike the nominal interest rate, APY shows exactly how much your money grows in a year, including the effect of interest earning interest — the power of compounding.
Banks advertise APY on savings accounts and CDs because it is always higher than the nominal rate (assuming compounding happens more than once per year). The more frequently interest compounds, the higher the APY. Daily compounding yields slightly more than monthly, which yields more than quarterly, and so on.
This calculator converts any nominal rate into APY based on your chosen compounding frequency. It also projects your savings growth over time, including regular monthly additions. Use the comparison table to see exactly how much difference compounding frequency makes — and understand why APY is the number that truly matters for your savings.
When This Page Helps
When comparing savings accounts, CDs, or money market funds, APY is the cleanest way to compare yield because it includes compounding. This calculator shows how much extra return comes from compounding frequency, so you can compare offers with the same nominal rate on an equal basis.
How to Use the Inputs
- Enter the nominal (stated) interest rate.
- Select the compounding frequency (daily, monthly, quarterly, etc.).
- Enter your initial deposit amount.
- Add any planned monthly contributions.
- Set the time horizon in years.
- Review APY and compare compounding frequencies in the table.
- Check the year-by-year growth projection.
Formula used
APY = (1 + r/n)^n − 1, where r = nominal annual rate (decimal), n = compounding periods per year. For continuous compounding: APY = e^r − 1.Example Calculation
Result: APY: 5.1162% — $10,000 grows to $26,491 in 5 years with $200/mo additions
A 5.0% nominal rate compounded monthly produces an APY of 5.1162% — the extra 0.1162% comes entirely from compounding. With $10,000 initial and $200/month over 5 years, total deposits are $22,000 and total interest earned is approximately $4,491.
Tips & Best Practices
- APY is always ≥ the nominal rate — the difference grows with higher rates and more frequent compounding.
- Daily vs monthly compounding on typical savings rates adds only a few basis points — focus on the rate itself.
- CDs often quote APY directly; savings accounts may show both nominal and APY.
- APY assumes you leave interest in the account (reinvest) — withdrawing interest reduces actual returns.
- For comparing loan costs, use APR (Annual Percentage Rate); for comparing savings, use APY.
- At very high rates, the compounding frequency difference becomes more significant.
Why APY Matters
APY converts a stated interest rate into the actual annual yield after compounding. That makes it the right comparison tool for deposit accounts and other savings products where interest is credited back into the balance.
Compounding Frequency
The more often interest is added to the account, the sooner it starts earning its own interest. Daily compounding produces a slightly higher return than monthly or quarterly compounding, though the difference is usually small at everyday savings rates.
Comparing Offers
Use APY to compare accounts with different compounding schedules, but still check the underlying rate, minimum balance rules, fees, and withdrawal restrictions. A slightly higher APY is only valuable if the account terms also fit how you plan to use the money.
Sources & Methodology
Last updated:
Methodology
This page converts the entered nominal annual rate into an annual percentage yield using the selected compounding frequency, then projects growth by adding the initial deposit and monthly contributions period by period before crediting interest for that period. It also shows a comparison table so the user can see how the same nominal rate translates into different effective yields at annual, semiannual, quarterly, monthly, daily, and continuous compounding.
It is a planning worksheet rather than a bank disclosure statement. Actual account earnings can differ because institutions may quote only APY, apply balance tiers, charge fees, require minimum balances, or limit withdrawals, while this page assumes a constant nominal rate and uninterrupted reinvestment.
Sources
- Appendix A to Part 1030 - Annual Percentage Yield Calculation (Consumer Financial Protection Bureau) — Primary Regulation DD formula for APY disclosures and advertising.
- Truth in Savings - Annual percentage yield (§ 1030.2(c)) (Federal Deposit Insurance Corporation) — FDIC examination manual definition of APY as interest plus compounding over a 365-day period under Regulation DD.
Frequently Asked Questions
APY (Annual Percentage Yield) reflects earnings with compounding — used for savings and investments. APR (Annual Percentage Rate) reflects borrowing costs including fees — used for loans. APY will always be ≥ the nominal rate; APR will always be ≥ the interest rate.
More frequent compounding means interest is calculated on a shorter period and added to the balance sooner, where it begins earning interest itself. Daily compounding yields slightly more than monthly, which yields more than quarterly or annually.
Yes, assuming all other terms are equal. A higher APY means more interest earned. However, consider withdrawal restrictions, FDIC insurance limits, minimum balance requirements, and account fees when comparing options.
Continuous compounding is the theoretical limit where interest compounds infinitely often. The formula is APY = e^r − 1. In practice, daily compounding is very close to continuous compounding and the difference is negligible for most rates.
No. APY only reflects the interest rate and compounding frequency. Account fees, maintenance charges, or penalties for early withdrawal are not included. Always check the full fee schedule alongside the APY.
At 5% for 1 year: annual compounding yields $500; monthly yields $511.62; daily yields $512.67. The difference is modest for one year but compounds significantly over longer periods. Over 20 years, the gap widens to hundreds or thousands of dollars.
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