What’s the difference between APR and APY?

APR (Annual Percentage Rate) is usually a nominal annual rate. It tells you the stated yearly rate before you consider how often interest is applied (compounded). Many products quote APR because it’s a simple headline number.

APY (Annual Percentage Yield) is the effective annual rate. It answers: “If interest compounds throughout the year, what is my actual annual growth rate?” APY incorporates compounding, so it’s the better “apples-to-apples” number when comparing savings accounts, CDs, and other interest-bearing accounts.

• Let r be the APR as a decimal (12% = 0.12) and n be the number of compounding periods per year.
• APY (effective annual rate) = (1 + r/n)ⁿ − 1
• If compounding is annual (n = 1), APY equals APR. As n increases, APY rises above APR.

• If you know APY and compounding, you can solve for APR: APR = n × [(1 + APY)^1/n − 1]

For loans, the “true” cost can be higher than the advertised APR because of fees (origination, processing, etc.). A simplified way to estimate the effective rate is to model cash flows:

• You receive net proceeds = loan amount − upfront fees.
• You repay equal monthly payments calculated from the advertised APR.
• The effective APR is the rate that makes those cash flows break even (an IRR calculation).

That’s exactly what this tool does in “Borrowing” mode: it computes the standard payment from the stated APR, then finds the implied effective rate after subtracting fees from the amount you actually receive.

Two quick examples (with intuition)

Example 1: Savings account at 5.00% APR, monthly compounding.

• r = 0.05, n = 12
• APY = (1 + 0.05/12)¹² − 1 ≈ 5.12%
• Why higher? You earn interest on previously earned interest each month.

Example 2: Loan at 12.00% APR, 24 months, 2% origination fee.

• You borrow $10,000 but only receive $9,800 after the fee.
• Your monthly payment is calculated from 12% APR (monthly rate = 1%).
• The effective APR is higher because the lender’s cash outflow is smaller (you received less), but your repayment schedule is the same.

In real disclosures, some fees may be included or excluded depending on product and regulation. Use the estimate to compare offers fast, then verify with the official truth-in-lending / account disclosure.

Behind the scenes (what the calculator actually computes)

This calculator has two “brains” depending on the scenario you pick:

• Converts your input APR to a decimal (e.g., 12.99% → 0.1299).
• Uses the compounding conversion: (1 + r/n)ⁿ − 1.
• Returns APY as a percentage, rounded sensibly for readability.

• Computes the monthly payment from the stated APR and term using the standard amortization formula.
• Subtracts the upfront fee from the amount you actually receive.
• Finds the monthly rate that makes the present value of payments equal your net proceeds (an IRR / root-find).
• Reports:
  • Effective APR (annualized from the monthly IRR)
  • Equivalent APY from that effective APR (so you can compare cost vs yield consistently)

Want max clarity? Use borrowing mode for loans/credit offers and savings mode for deposit accounts. Then compare the effective numbers.

Frequently Asked Questions

• Is APY always higher than APR?

  If interest compounds more than once per year, APY will be higher than the nominal APR for savings. If compounding is annual (once per year), APY equals APR. For borrowing, “APY” isn’t the typical disclosure term, but we show an equivalent effective rate to make comparisons easier.

• Why do two loans with the same APR cost different amounts?

  Fees, payment timing, and compounding conventions can change the real cost. A 0% origination fee vs a 3% fee can meaningfully shift the effective APR—even if the advertised APR is identical.

• What compounding should I choose?

  For most savings accounts, daily compounding is common, but the bank may still quote APY directly. For loans, monthly is typical for payment schedules. If you’re unsure, use Monthly as a practical default for comparing consumer loans.

• Is this the same as EAR (Effective Annual Rate)?

  Yes. APY is essentially the effective annual rate for savings. Different industries use different labels (APY, EAR, effective rate), but the core compounding idea is the same.

• Does APR include all fees?

  Not always. Some fees are included in official APR calculations, others may not be (depending on product, regulation, and fee type). That’s why this tool lets you model an upfront fee explicitly—to see the “what-if” impact quickly.