Interest Rate Converter -- APR to APY & More

Understanding APR vs APY

The most important distinction in interest rates is between APR (Annual Percentage Rate) and APY (Annual Percentage Yield, also called EAR -- Effective Annual Rate). They describe the same underlying rate from two different perspectives.

APR is the nominal (stated) annual rate. It does not account for compounding. If a bank says "6% APR compounded monthly," they mean you earn 0.5% per month (6%/12). But because each month's interest earns interest in subsequent months, the actual amount you earn over a year is slightly more than 6%.

APY is the effective annual rate after compounding is included. It tells you what you actually earn (or owe) over one year. A 6% APR compounded monthly gives an APY of 6.168%.

Banks advertise APY on savings accounts (because it looks higher) and APR on loans (because it looks lower). When comparing financial products, always convert to the same rate type first.

Key Conversion Formulas

APR to APY (with compounding frequency n):

APY = (1 + APR/n)ⁿ - 1

APY to APR:

APR = n x [(1 + APY)^1/n - 1]

Continuous compounding (APR to APY):

APY = e^r - 1

Continuous rate from APY:

r_continuous = ln(1 + APY)

Periodic rate:

r_periodic = APR / n

Where n is the number of compounding periods per year (12 for monthly, 365 for daily, etc.), r is the rate expressed as a decimal, and e is Euler's number (~2.71828).

Worked Example: 6% APR Compounded Monthly

Suppose a savings account advertises 6% APR compounded monthly. What is the effective annual rate?

1. Identify the values: APR = 6% = 0.06, n = 12 (monthly)
2. Calculate periodic rate: 0.06 / 12 = 0.005 (0.5% per month)
3. Apply the formula: APY = (1 + 0.005)¹² - 1
4. Compute: APY = (1.005)¹² - 1 = 1.06168 - 1 = 0.06168
5. Result: APY = 6.168%

This means $10,000 deposited for one year earns $616.78 (not $600.00). The extra $16.78 comes from earning interest on interest each month.

When Does Compounding Frequency Matter Most?

The impact of compounding frequency depends on two factors: the interest rate and the time period.

• Low rates (1-3%): Compounding frequency makes almost no difference. A 2% APR gives 2.02% APY whether compounded monthly or daily.
• Medium rates (5-10%): The difference becomes noticeable. A 10% APR gives 10.47% APY monthly vs 10.52% APY daily -- a $50 difference per $100,000.
• High rates (15-30%): Compounding frequency matters significantly. A 24% APR (typical credit card) gives 26.82% APY monthly vs 27.11% APY daily. On $10,000 of debt, that is $29 more interest per year.

For most savings accounts and loans, the difference between monthly and daily compounding is small. But the difference between annual and monthly compounding can be substantial.

Frequently Asked Questions

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal rate -- the stated rate before considering compounding. APY (Annual Percentage Yield) is the effective rate after compounding. A 12% APR compounded monthly results in a 12.683% APY. Banks show APY on savings (looks higher) and APR on loans (looks lower). Always compare the same type when shopping for financial products.

How do I convert APR to APY?

Use APY = (1 + APR/n)ⁿ - 1, where n is compounding periods per year. For monthly compounding (n=12), a 6% APR becomes (1 + 0.06/12)¹² - 1 = 6.168% APY.

How do I convert APY to APR?

Use APR = n x [(1 + APY)^1/n - 1]. For example, 5% APY with monthly compounding: APR = 12 x [(1.05)^1/12 - 1] = 4.889%.

What is continuous compounding?

Continuous compounding is the theoretical limit where interest compounds every instant, using Euler's number (e ~ 2.71828). The formula is APY = e^r - 1. A 6% continuous rate gives an APY of e^0.06 - 1 = 6.184%. It produces slightly more than daily compounding and is used mainly in financial mathematics and derivatives pricing.

What is the monthly interest rate for a 6% APR?

The monthly rate is APR / 12 = 6% / 12 = 0.5% per month. This is the periodic rate applied each month. When compounded over 12 months, 0.5% monthly produces an effective annual rate (APY) of 6.168%.

Why do banks show APY for savings and APR for loans?

Marketing incentives. For savings, APY is higher than the nominal rate, making yields appear more attractive. For loans, APR is lower than APY, making borrowing costs appear smaller. Regulations require specific disclosures (APR for loans under Truth in Lending Act, APY for deposits under Truth in Savings Act).

How does compounding frequency affect the effective rate?

More frequent compounding produces a higher effective rate. A 10% APR gives an APY of 10.0% annually, 10.25% quarterly, 10.47% monthly, 10.516% daily, and 10.517% continuously. The marginal benefit decreases -- going from annual to monthly is significant, but monthly to daily is tiny.

Does this tool store my data?

No. All calculations happen entirely in your browser using JavaScript. No data is sent to any server, no cookies are set, and nothing is stored.

Privacy & Limitations

• Client-side only. No data is sent to any server. All calculations run in your browser.
• Assumes fixed rates. Real-world rates vary over time. This tool models constant rates for comparison purposes.
• Does not account for fees or taxes. Actual returns depend on account fees, tax treatment, and other factors.
• Not financial advice. This is an educational tool. Consult a qualified financial professional for investment or borrowing decisions.
• Reference rates are approximate. Typical rates shown are general market ranges and may not reflect current offerings.

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