APY Calculator

Calculate APY (Annual Percentage Yield) from a nominal rate (APR) and compounding frequency. Optionally estimate balance growth with deposits and a mini chart.

Background

APY reflects how compounding increases your effective yearly return. The more often interest compounds, the higher the APY (for the same nominal APR).

Enter your inputs

Mode:

Compute APY from APR + compounding

Compute APR from APY + compounding

Estimate balance growth (APY/APR + deposits)

Compounding frequency

APR / nominal rate (%)

Enter a percent (e.g., 5 = 5%). Can be 0 or higher.

APY (%)

Enter a percent (e.g., 5.12 = 5.12%). Must be ≥ 0.

Options:

Show step-by-step

Show effective annual factor (1 + APY)

Show per-period rate

Result:

No results yet. Enter a value and click Calculate.

How to use this calculator

Choose a mode: compute APY, compute APR, or estimate growth.
Select a compounding frequency (monthly/daily/continuous/custom).
Enter the rate, then click Calculate.

How this calculator works

For periodic compounding: APY = (1 + r/n)^n − 1
For continuous compounding: APY = e^r − 1
For growth: simulates period-by-period compounding and deposits.

Formula & Equation Used

Periodic: APY = (1 + r/n)^n − 1

Continuous: APY = e^r − 1

Note: “APR” here is the nominal annual rate; APY accounts for compounding.

Example Problems & Step-by-Step Solutions

Example 1 — Find APY from APR (monthly compounding)

A savings account advertises APR = 5.00% compounded monthly (n = 12). What is the APY?

Step-by-step

Convert APR to a decimal: r = 5.00% = 0.0500
Use the periodic compounding APY formula: APY = (1 + r/n)^n − 1
Plug in values (n = 12): APY = (1 + 0.0500/12)^{12} − 1
Compute: APY ≈ (1.0041667)^{12} − 1 ≈ 0.0511619
Convert to percent: APY ≈ 5.116%

Answer: The account’s APY is about 5.116%.

Example 2 — Find APR from APY (daily compounding)

You see a product with APY = 4.50% and it compounds daily (n = 365). What nominal APR does that correspond to?

Step-by-step

Convert APY to decimal: APY = 4.50% = 0.0450
Start from: 1 + APY = (1 + r/n)^n
Solve for r: r = n[(1 + APY)^{1/n} − 1]
Plug in values: r = 365[(1.0450)^{1/365} − 1]
Compute (approx.): r ≈ 0.04402 → APR ≈ 4.402%

Answer: The nominal APR is about 4.40% (daily compounding).

Example 3 — Growth estimate with monthly deposits

You deposit \$1,000 today into an account with APR = 4.50% compounded monthly. You also add \$100 per month. Estimate the balance after 3 years.

Step-by-step

Convert APR to decimal: r = 4.50% = 0.0450
Monthly compounding means: n = 12 and per-month rate i = r/n = 0.0450/12 = 0.00375
Total months: t = 3 years → 36 months
Growth of the initial \$1,000: FV₀ = 1000(1 + i)^{36}
Growth of monthly deposits (ordinary annuity approximation): FV_d = 100 \cdot \frac{(1+i)^{36} - 1}{i}
Add them: FV ≈ FV₀ + FV_d

Answer (estimate): The calculator will simulate period-by-period and should land around \$4,800–\$4,900 depending on the deposit timing assumption.

Note: The calculator’s “Growth mode” assumes deposits happen at the start of each period, then interest applies. (Some banks assume end-of-period deposits; results will be slightly lower.)