APY formula (Annual Percentage Yield)

If the nominal annual rate is r and interest compounds n times per year, then the effective annual yield is:

• APY = (1 + r/n)ⁿ − 1

This calculator also estimates balance growth over multiple years by applying the periodic rate i = r/n over N = n × years compounding periods.

• Same r, higher n → slightly higher APY.
• APY is best for comparing savings yields; APR is usually used for borrowing costs.
• For large balances and long horizons, even small APY differences can matter.

Fast examples you can copy

• 5% nominal, monthly compounding: APY ≈ 5.12%
• 5% nominal, daily compounding: APY ≈ 5.13%
• Try this: set principal = $10,000 and years = 1, then switch monthly ↔ daily and screenshot the difference.

Want the “viral” version? Post a before/after comparing two bank APYs and ask: “Which one would you pick?”

APY Calculator: understand your real annual yield (Omni-level guide)

APY (Annual Percentage Yield) is the “real” yearly return on an interest-bearing account when you include compounding. It’s the number that answers the question: “If I leave money here for a year, what percentage will my balance actually grow?” Banks and brokerages often advertise both an interest rate (APR / nominal rate) and an APY. APY is usually the one you want for comparing savings accounts, money market funds, CDs, and even some lending products.

Why? Because compounding means you earn interest on your interest. The more frequently interest compounds (daily vs monthly vs yearly), the higher your effective annual return becomes—even if the advertised nominal rate stays the same. This calculator helps you convert a nominal rate + compounding frequency into APY and also shows how that APY plays out on a real balance over time.

1) The core APY formula (the one banks use)

Let:

• r = nominal annual interest rate (APR-like), as a decimal (e.g., 5% → 0.05)
• n = number of compounding periods per year (365 daily, 12 monthly, 4 quarterly, 1 yearly)

Then:

APY = (1 + r/n)ⁿ − 1

This gives the effective annual yield, assuming the interest compounds at a steady schedule and you leave the funds in place the whole year. Two important notes:

• APY is always ≥ the nominal rate when compounding happens more than once per year.
• When n = 1 (annual compounding), APY equals the nominal rate.

2) APR vs APY (quick mental model)

• APR (nominal rate): the “sticker” rate per year, not accounting for compounding.
• APY (effective yield): the rate you effectively earn over a year including compounding.

If you’re shopping between accounts, APY makes comparisons fair. Two banks may both advertise 5.00% nominal, but the one that compounds daily will typically have a slightly higher APY than the one that compounds monthly.

3) Turning APY into real money (future value with compounding)

APY is a percentage. To see dollars, you need a growth model. This calculator supports:

• One-time initial deposit (principal)
• Optional periodic contribution (monthly, weekly, daily, etc.)
• Time horizon in years

We compute growth using a periodic interest rate:

i = r / n (interest per compounding period)

Number of compounding periods over the full horizon:

N = n × years

Initial deposit growth:

FV_principal = P × (1 + i)^N

Contributions are modeled as an ordinary annuity (payments at the end of each period). If your contribution frequency matches the compounding frequency (for example, monthly contributions with monthly compounding), then:

FV_contrib = PMT × [((1+i)^N − 1) / i]

If the contribution frequency is different (for example, monthly contributions with daily compounding), we convert the contribution cadence into an “effective rate per contribution period.” That lets us approximate the annuity growth in a way that feels realistic for most consumer use-cases.

4) Examples (so you can sanity-check the results)

Example A: 5% nominal rate compounded monthly
r = 0.05, n = 12.
APY = (1 + 0.05/12)¹² − 1 ≈ 0.05116 → 5.12% APY.
If you deposit $10,000 for 1 year with no additional contributions, your ending balance is about $10,511.62.

Example B: same 5% rate but compounded daily
r = 0.05, n = 365.
APY = (1 + 0.05/365)³⁶⁵ − 1 ≈ 0.05127 → 5.13% APY.
The difference is small, but over large balances or many years, the compounding schedule matters.

Example C: $200/month contributions for 5 years at 4.25% nominal, monthly compounding
This is where APY becomes useful for comparing accounts: a slightly higher APY can change the ending balance meaningfully when you add contributions. Plug in your own numbers and see the final value, total contributions, and interest earned.

5) How to use this calculator for “virality” and sharing

APY comparisons are perfect for quick, shareable “money clarity” posts because they turn confusing bank rate math into a single screenshot. Try these share-friendly mini-experiments:

• “Daily vs monthly compounding” at the same nominal rate and principal.
• “My savings plan”: add a monthly contribution and show your 1-year vs 5-year ending balance.
• “APR isn’t APY”: show how a nominal rate becomes a different APY depending on compounding.

6) Common pitfalls (and how to avoid them)

• Intro teaser rates: some accounts change rates after a promo period. APY assumes the rate stays constant.
• Fees and minimums: APY ignores account fees. A monthly fee can wipe out a small APY advantage.
• Taxes: interest is often taxable. Your after-tax yield can be lower.
• Timing of deposits: contributions at the start of the month vs end can slightly change outcomes.

7) FAQs

• What does APY stand for?

  APY stands for Annual Percentage Yield—the effective annual return including compounding.

• Is a higher APY always better?

  Usually, yes for savings/investment yields—but always check fees, withdrawal limits, and promo-rate fine print.

• Why is APY higher than the interest rate?

  Because compounding adds “interest on interest.” The more frequent the compounding, the higher the APY.

• Does APY apply to loans too?

  Loans typically emphasize APR (cost). But APY logic is still useful when a product advertises “effective” rates or compounding details.

• How accurate is the balance projection?

  It’s a solid estimate under a constant-rate assumption. Real accounts can change rates, and contribution timing can vary.

Educational note: This APY calculator is designed to help you compare rates and understand compounding. For major financial decisions, verify product disclosures and consider professional advice.