APY Calculator

Nominal rate to effective annual yield by compounding

Quick Answer

APY Calculator: Nominal rate to effective annual yield by compounding. APY = (1 + r/n)ⁿ − 1 (r = nominal rate, n = compounding periods/yr).

APR（nominal %）

Compounds/yr

Principal

APY（effective annual yield）

3.557%

¥10,000 earns ¥355.67/yr · continuous limit 3.562%

APR3.5%

APY3.557%

Yearly gain¥355.67

vs annual¥5.67

Steps

1APY = (1 + APR/n)ⁿ − 1
2APY = (1 + 3.5%/12)^12 − 1 = (1 + 0.002917)^12 − 1
3APY = 3.5567%
4Earnings = 10,000 × 0.03557 = ¥355.67

Frequency comparison

Frequency	APY	Yearly gain
Annually	3.500%	¥350.00
Semiannually	3.531%	¥353.06
Quarterly	3.546%	¥354.62
Monthly ←	3.557%	¥355.67
Daily	3.562%	¥356.18
Continuous	3.562%	¥356.20

💡 APR is the simple nominal rate; APY includes compounding — it's what you ACTUALLY earn. Savings ads show APY (bigger), loan ads show APR (smaller). Comparing products? Always convert both to APY. Monthly compounding at 3.5% APR ≈ 3.557% APY.

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How to Use

Enter amounts and terms: fill principal, rate and period in the APY Calculator (defaults work for a quick try).
Instant results: key figures and cost breakdown update live as you type.
Compare scenarios: tweak any parameter to compare costs and returns across plans.
Copy key numbers: one-click copy for records or sharing with your advisor.

Key Points

APY Calculator is a free online finance tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Nominal rate to effective annual yield by compounding.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

APR vs APY

APY = (1 + r/n)ⁿ − 1 (r = nominal rate, n = compounding periods/yr)

More frequent compounding → higher APY: monthly > quarterly > yearly

Continuous compounding limit: APY = e^r − 1

Compare deposits AND loans by APY for the true rate

Example: 4.8% nominal monthly → APY = (1+0.004)¹² − 1 ≈ 4.907%; continuous ≈ 4.917%.

FAQ

How do I use the APY Calculator?

Open the page and fill in the input fields — results update automatically. Nominal rate to effective annual yield by compounding.

Are the results accurate?

Yes. Standard financial formulas and published rate data are used. For official figures, consult your financial institution.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Can I use the results for financial decisions?

Results are for reference. Consult a licensed financial advisor before major decisions.

Does it work on mobile?

Yes. Fully responsive on phones, tablets and desktops.

Related Guides

Source & Updates

Based on published rate tables and standard financial formulas. Last updated: 2025-07

Authoritative sources:

Last updated: 2026-08-04

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. APY Calculator[EB/OL]. https://www.yijiansuan.com/en/c/finance/apy

Results provided by this tool are for reference only and do not constitute professional advice.