APY vs APR Comparison Calculator
Compare APY and APR to understand the true cost of borrowing or return on savings. See how compounding frequency affects your effective rate.
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor
APY vs APR Comparison Calculator
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Formula: APY = (1 + r/n)^n - 1
Worked example — APY: 4.867% | Interest earned: $3,825.09 | $262.59 more than simple interest
Formula
APY = (1 + r/n)^n - 1
Where r is the nominal annual interest rate (as a decimal), and n is the number of compounding periods per year (1 = annually, 4 = quarterly, 12 = monthly, 365 = daily). For continuous compounding, APY = e^r - 1. APY represents the true annual return accounting for compounding effects.
Worked Examples
Example 1: High-Yield Savings Account APY
Problem:A high-yield savings account offers 4.75% nominal rate compounded daily. Calculate the APY and interest earned on $25,000 over 3 years.
Solution:APY = (1 + 0.0475/365)^365 - 1 = (1.0001301)^365 - 1 = 1.04867 - 1 = 0.04867 = 4.867% Future Value = $25,000 x (1 + 0.0475/365)^(365 x 3) = $25,000 x 1.15300 = $28,825.09 Compound Interest = $28,825.09 - $25,000 = $3,825.09 Simple Interest would be = $25,000 x 0.0475 x 3 = $3,562.50 Compounding benefit = $3,825.09 - $3,562.50 = $262.59
Result:APY: 4.867% | Interest earned: $3,825.09 | $262.59 more than simple interest
Example 2: CD Rate Comparison
Problem:Bank A offers a 5.00% CD compounded monthly. Bank B offers 4.95% compounded daily. Which gives a higher effective yield?
Solution:Bank A APY = (1 + 0.05/12)^12 - 1 = (1.004167)^12 - 1 = 0.05116 = 5.116% Bank B APY = (1 + 0.0495/365)^365 - 1 = (1.0001356)^365 - 1 = 0.05074 = 5.074% Bank A has a higher APY (5.116% vs 5.074%) On $50,000 over 1 year: Bank A earns: $50,000 x 0.05116 = $2,558.13 Bank B earns: $50,000 x 0.05074 = $2,537.13 Difference: $20.99
Result:Bank A (5.116% APY) beats Bank B (5.074% APY) by $20.99 per year on $50,000
Frequently Asked Questions
What is APY and how is it different from APR?
APY (Annual Percentage Yield) is the effective annual rate of return that accounts for the effect of compounding interest, while APR (Annual Percentage Rate) is the nominal rate without considering compounding. APY is always equal to or higher than APR for the same nominal rate when compounding occurs more than once per year. For example, a savings account with a 5% APR compounded monthly has an APY of 5.116%, meaning you actually earn 5.116% on your money annually, not just 5%. Banks are required by the Truth in Savings Act to disclose APY on deposit accounts, making it easier for consumers to compare products. For loans, APR is the standard disclosure under the Truth in Lending Act, which can make comparing savings and loan rates confusing.
How is APY calculated mathematically?
APY is calculated using the formula APY = (1 + r/n)^n - 1, where r is the nominal annual interest rate expressed as a decimal and n is the number of compounding periods per year. For monthly compounding with a 5% nominal rate: APY = (1 + 0.05/12)^12 - 1 = (1.004167)^12 - 1 = 0.05116 or 5.116%. For daily compounding: APY = (1 + 0.05/365)^365 - 1 = 5.127%. For continuous compounding, the formula becomes APY = e^r - 1, where e is Euler's number (approximately 2.71828). This gives the theoretical maximum APY for any given nominal rate. The difference between monthly and daily compounding is typically small, but for large balances or high rates, even small APY differences can represent significant dollar amounts over time.
Why does compounding frequency matter for APY?
Compounding frequency determines how often earned interest is added back to the principal, where it then begins earning interest itself. More frequent compounding means interest starts earning its own interest sooner, resulting in a higher effective yield. Consider $100,000 at 6% nominal rate over one year: with annual compounding, you earn $6,000. With monthly compounding, you earn $6,167.78 because each month's interest (starting at $500) is added to the principal and earns additional interest in subsequent months. With daily compounding, you earn $6,183.13. The difference between annual and daily compounding on $100,000 at 6% is $183.13 per year. While this may seem modest for one year, over decades of investing, the compounding frequency effect accumulates substantially through the exponential nature of compound growth.
How does APY affect savings account and CD comparisons?
When comparing savings accounts and certificates of deposit, APY is the most reliable metric because it normalizes different compounding frequencies into a single comparable number. A savings account offering 4.5% compounded daily actually yields an APY of 4.603%, while a CD offering 4.55% compounded monthly yields an APY of 4.645%. Without calculating APY, you might incorrectly choose the 4.5% daily account over the 4.55% monthly CD. Online high-yield savings accounts often compound daily and advertise their APY prominently, while traditional banks may compound monthly or quarterly. Some promotional rates compound annually, significantly reducing the effective yield. Always compare APY to APY, not nominal rates, and remember to also consider minimum balance requirements, withdrawal penalties for CDs, and fee structures.
What is the relationship between APY and the Rule of 72?
The Rule of 72 provides a quick approximation for how long money takes to double at a given APY. Divide 72 by the APY percentage to estimate doubling time in years. At 4% APY, money doubles in approximately 72 divided by 4 equals 18 years. At 6% APY, it takes about 12 years. At 8% APY, roughly 9 years. However, the Rule of 72 uses the nominal rate in its simplest form, and for precise calculations you should use the exact formula: doubling time equals ln(2) divided by n times ln(1 + r/n), where ln is the natural logarithm. The Rule of 72 is most accurate for rates between 6% and 10%. For very low rates below 4%, the Rule of 69.3 provides better accuracy, while for higher rates above 20%, the Rule of 72 progressively overestimates the doubling time.
References
Reviewed for accuracy by Sahil, Senior Finance & Tax Editor · Editorial policy
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