Convert an advertised CD APY back to its APR.
Rate is quoted as
1 year
Common terms
Compounding frequency
$10,000.00 in a 1 year CD at 4.60% APY, compounded daily, grows to $10,460.00 — that’s $460.00 of interest, averaging $38.33 per month.
Balance over the term
| Month | Principal | Interest | Balance |
|---|---|---|---|
| At opening | $10,000.00 | $0.00 | $10,000.00 |
| 2mo | $10,000.00 | $75.24 | $10,075.24 |
| 5mo | $10,000.00 | $189.16 | $10,189.16 |
| 7mo | $10,000.00 | $265.82 | $10,265.82 |
| 10mo | $10,000.00 | $381.89 | $10,381.89 |
| 1y | $10,000.00 | $460.00 | $10,460.00 |
Calculated in your browser using A = P(1 + r/n)nt. Nothing is sent to a server. Figures are before tax; confirm exact terms with your bank.
Formulas and content last reviewed . Bank rates change frequently — confirm current rates directly with your institution.
The short answer
A CD's APR is its nominal annual rate before compounding — the rate actually applied at each compounding period — and it converts from APY as APR = n × ((1 + APY)^(1/n) − 1). A 4.60% APY compounded daily corresponds to a 4.50% APR. You need this conversion whenever a bank quotes you a nominal or "interest rate" figure rather than APY, because entering a nominal rate into a calculator expecting APY applies compounding twice and overstates your return. It also matters when comparing a CD against a product quoted in APR, such as a loan you might otherwise pay down. APR is always the lower of the two numbers on any account compounding more than once a year, which is why marketing leads with APY, and why Regulation DD makes APY the required disclosure.
Formula & method
APR = n × ((1 + APY)^(1/n) − 1)
Strips the compounding effect back out of an advertised yield.
Convert the advertised APY to a decimal (4.60% → 0.046).
Add 1 to get the annual growth factor.
Take the n-th root — raise it to the power of 1 ÷ n.
Subtract 1 to get the rate for a single compounding period.
Multiply by n and by 100 for the annualised nominal rate.
Guide
Type the bank's quoted figure and set the toggle to APY, which is how deposit rates are normally published.
This drives the conversion. Daily compounding creates the largest gap between APY and APR.
The result card shows APY and APR together, so you can see precisely what compounding contributes.
Examples
Inputs
Result
The bank credits interest at a 4.50% annual rate; daily compounding is what lifts the effective yield to 4.60%.
Methodology
APR here means the nominal deposit rate. On loans, APR also includes fees — that is a different calculation entirely.
The conversion assumes interest compounds at the stated frequency and stays in the account.
A 365-day year is used, consistent with Regulation DD.
Conventions follow Regulation DD (12 CFR 1030), which governs how US institutions disclose APY on deposit accounts. Deposits at insured institutions are FDIC-protected up to $250,000 per depositor, per bank, per ownership category.
Primary sources
Details
For deposits, APY > APR whenever interest compounds more than once a year. For loans the relationship is reversed in effect, because fees inflate loan APR.
If a bank quotes only an 'interest rate' with no APY label, treat it as the nominal APR and convert before comparing.
The APY–APR gap scales with the rate: about 0.01 points at 1%, roughly 0.13 points at 5%.
If your CD pays interest out monthly rather than compounding it, your realised return matches the APR, not the APY.
How it connects
Applications
You want to know the mechanics behind the advertised number rather than take it at face value.
You are building your own projection and need the nominal rate to feed a period-by-period model.
Related tools
FAQs
APR = n × ((1 + APY)^(1/n) − 1), where APY is the quoted yield as a decimal and n is the number of compounding periods per year. It converts an effective annual yield back into the nominal rate that is actually applied at each compounding period. A 4.60% APY compounded daily corresponds to a 4.50% APR. You need this conversion whenever a bank hands you an APY but a calculator, a spreadsheet or a comparison expects a nominal rate — entering an APY where a nominal rate belongs applies compounding a second time and overstates the result. APR is always the lower of the two figures on any account compounding more than once a year, and the gap widens as the rate and the compounding frequency rise. It is the rate the bank works with internally; APY is the rate it advertises.
Security & privacy
Uses the same compound interest and APY conventions as banks under Regulation DD.
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Every advertised APY has a nominal APR underneath it. Convert yours and see exactly what compounding is adding.