APR to APY Calculator
Understanding APR and APY
APR, or Annual Percentage Rate, indicates the simple interest cost of a loan or the return on an investment over a year without taking compounding into account. APY, or Annual Percentage Yield, includes the effect of compounding, showing the true rate at which money grows or debt accrues when interest is periodically added to the balance. The difference between APR and APY can be significant, especially when interest compounds multiple times per year. This calculator converts between these two commonly used rates so you can compare financial products on equal footing.
Knowing how to convert APR to APY is valuable when evaluating savings accounts, certificates of deposit, or other interest-bearing investments. Banks often advertise APY so consumers can easily see how much a deposit will grow. Conversely, credit cards and loans typically quote APR, giving borrowers a sense of the annualized cost. Converting between these metrics allows you to understand the real impact of compounding and choose the option that best suits your needs.
The conversion formulas (with MathML)
If an APR is compounded times per year, the effective annual yield is:
Solving the same relationship for APR gives:
The important takeaway is that APY depends on compounding frequency. The more often interest is added, the more APY exceeds APR for the same nominal rate.
How to Use the Calculator
Begin by entering the interest rate as a percentage, such as 5 for five percent. Next, input the number of compounding periods per year. Common values are 12 for monthly, 4 for quarterly, or 365 for daily. Finally, select whether you are converting from APR to APY or from APY to APR. Click Calculate, and the script will apply the appropriate formula to display the converted rate. The result reveals how the frequency of compounding changes the effective rate of return or interest cost.
If you are converting APR to APY, the formula used is APY = (1 + APR/periods)^(periods) - 1. This equation shows how compound interest increases the effective yield beyond the simple APR value. Conversely, when converting APY to APR, the formula rearranges to APR = periods * ((1 + APY)^(1/periods) - 1). By performing these calculations automatically, the calculator saves you the trouble of manipulating exponents or remembering complex equations.
Why Compounding Matters
Compounding refers to the process of earning interest on previously earned interest. When money is compounded frequently, growth accelerates because each compounding period adds a small amount to the balance, which then earns interest in subsequent periods. This compounding effect can make a noticeable difference over time, especially with higher interest rates or longer investment horizons. Understanding how often interest compounds is crucial when comparing financial products, as a seemingly small difference in rate can translate into significant gains or costs.
For borrowers, frequent compounding means paying more over the life of a loan. Credit cards, for example, often compound daily, resulting in more interest accruing if balances are not paid in full. On the other hand, savers benefit from more frequent compounding, as their deposits grow faster. Being able to convert between APR and APY helps clarify which products provide better value and prevents surprises down the line.
Practical Examples
Imagine you have a certificate of deposit with a 4% APR that compounds monthly. Using the APR to APY conversion, you find the APY is approximately 4.07%. That slight increase reflects the extra earnings generated each month. Conversely, if a savings account lists an APY of 1.5% with daily compounding, you can determine the equivalent APR is slightly less, about 1.49%. These small differences add up over large balances or long periods, so converting rates helps you compare offers accurately.
The calculator is also useful for loans. If a lender quotes an APY on a personal loan, but you want to know the APR to compare it with other lenders, simply enter the APY and compounding frequency. The resulting APR reflects the base interest rate before compounding effects, allowing an apples-to-apples comparison. Whether you are saving or borrowing, understanding both metrics ensures you fully grasp the financial implications.
Tips for Accurate Conversions
Ensure you know the correct number of compounding periods per year. Misunderstanding whether a rate compounds daily or monthly can lead to inaccurate results. When in doubt, ask the financial institution or read the account disclosures carefully. Also, use a decimal format for the rate input if necessary—many people find it easier to type 6.5 rather than 6.50. The calculator will handle either format and display the result with two decimal places for clarity.
Keep in mind that banks sometimes use terms like "nominal rate" or "effective rate." The nominal rate is essentially the APR, while the effective rate corresponds to APY. By converting between them, you ensure you are comparing equivalent values even when terminology differs. This awareness can help you spot deals that appear attractive at first glance but may offer less value once compounding is considered.
Conclusion
Whether you are evaluating a mortgage, shopping for a high-yield savings account, or comparing credit cards, understanding the relationship between APR and APY is vital. This calculator simplifies the conversion process so you can focus on choosing the right financial product. By seeing how compounding changes the effective rate, you gain insight into the true cost of borrowing or the real return on your investment. Use the tool whenever you encounter interest rates to make well-informed decisions and maximize your financial outcomes.
Common compounding periods
Financial products often compound on standard schedules. Use this table to choose the correct “compounds per year” value when disclosures use plain language like “monthly” or “daily”.
| Disclosure wording | Periods per year (n) | Where it appears |
|---|---|---|
| Annually | 1 | Some bonds, simple products |
| Semiannually | 2 | Bonds, CDs |
| Quarterly | 4 | Some savings products |
| Monthly | 12 | Many savings accounts, loans |
| Weekly | 52 | Some retail products |
| Daily | 365 | Credit cards, many deposit accounts |
APR/APY vs. balances and timelines
APR and APY describe rates, not dollars. To translate rates into money, you need a principal amount and a timeframe. This calculator includes optional “principal” and “years” fields to show the compounded growth rate and an approximate final value when the rate is applied consistently for the full duration. In the real world, balances can change (deposits, withdrawals, payments), so treat the dollar outputs as a simple scenario rather than a perfect forecast.
Limitations
This page models periodic compounding at a fixed nominal rate. It does not model variable rates, teaser periods, rate caps, minimum balance rules, or fees that can overwhelm interest earnings. Always read disclosures and compare net outcomes after fees.
Quick intuition: why APY is always ≥ APR (when APR ≥ 0)
With positive interest rates, compounding adds interest-on-interest. If you compound once per year, APR and APY match. If you compound more frequently, you credit interest earlier, which increases the effective annual yield. That is why banks tend to advertise APY: it is the “apples to apples” number for growth over a year.
For borrowers, the same principle increases the effective cost when compounding is frequent. That’s why a credit card with daily compounding can feel more expensive than the nominal APR suggests when balances are carried for long periods.
Related calculators
To compare interest products more broadly, see the Percentage Calculator, the Compound Interest Calculator, and the Mortgage Calculator.