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APR ↔ APY Converter

Real rate · After-tax yield · Fee drag · Scenario analysis · Wealth projector

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$
By Jan 2031
💸 Fees & Costs
$
$
📊 Real Return & Tax
Inflation Rate 3.0%
Tax Rate 22%
EFFECTIVE APY
5.116%
Earns $511.62/yr. +$11.62 extra vs simple interest.
Effective APY
5.116%
Real APY
2.053%
After-Tax APY
3.991%
Doubling Time
~14.1 yrs
Total Interest
$2,833.59
Compounding Bonus
+$82.92
APY = (1 + r/n)ⁿ − 1 n = 12 periods/yr After-Tax = APY × (1 − τ)
Chart: effective apy.
Chart: effective apy.
💸 Open Fees & Costs and enter an annual or upfront fee to see its impact on your APY.
Period Balance Earned Cum. Interest Real Value
🐻 Bear · Base · 🐂 Bull Scenarios (Rate ±25%)
🐻 Bear (−25%)
APR—
APY—
Real APY—
After-Tax APY—
Final Value—
Compounding Bonus—
📍 Base (Current)
APR—
APY—
Real APY—
After-Tax APY—
Final Value—
Compounding Bonus—
🐂 Bull (+25%)
APR—
APY—
Real APY—
After-Tax APY—
Final Value—
Compounding Bonus—
🔢 APY by APR × Compounding Frequency
Switch to this tab to load the matrix.
📊 Market Rate Comparison
Chart: 🐻 bear (−25%).
🎯 Goal Seeker
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$
🪜 APY Rate Ladder — Cost of Every 1%
APY 5 Years 10 Years 20 Years 30 Years
📈 30-Year Growth Projection
Chart: apr↔apy converter.
🌡️ Inflation Erosion — Purchasing Power Over Time
Period Nominal Balance Real Balance Purchasing Power Lost
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How to Use This Calculator

1

Choose Mode

Select Find APY to see the effective yield from a nominal APR, or Find APR to find the required nominal rate for a target APY. Load a preset for common scenarios.

2

Enter Your Details

Input your rate, compounding frequency, principal, and time period. Optionally open the Fees & Costs and Real Return & Tax sections for deeper analysis.

3

Explore All Tabs

Use Scenario Analysis to compare Bear/Base/Bull and market rates. Use Wealth Projector to set goals, compare 30-year growth, and see inflation's long-term impact.

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Frequently Asked Questions

Basics What is the main difference between APR and APY?
APR represents the annual rate of interest without taking into account the compounding of interest within that year. APY, on the other hand, does take into account the effects of compounding, providing a more accurate representation of the total interest earned or paid over a year.
Basics What is Real APY and why does it matter?
Real APY is the inflation-adjusted yield, calculated using the Fisher equation: Real APY = ((1 + APY) / (1 + inflation)) − 1. If your savings account pays 4% APY but inflation is 3.5%, your real gain in purchasing power is only about 0.48%. This is the truest measure of wealth growth.
Strategy How do fees reduce my effective APY?
Annual maintenance fees and upfront origination fees reduce the net value of your investment or savings. A $10/month fee on a $10,000 savings account at 4% APY reduces your effective yield by roughly 1.2%, leaving you with only ~2.8% net APY. Always consider fee-free alternatives when available.
Basics What is After-Tax APY?
After-Tax APY is your yield after paying income taxes on interest. It equals APY × (1 − tax rate). If your APY is 5% and you're in the 22% tax bracket, your after-tax APY is only 3.9%. Tax-advantaged accounts (Roth IRA, 401k) can eliminate this drag entirely.
Strategy How can I convert APR to APY?
Use the formula: APY = (1 + r/n)^n − 1, where 'r' is the APR as a decimal and 'n' is the number of compounding periods per year. For continuous compounding: APY = e^r − 1.
Basics What is 'Continuous Compounding'?
Continuous compounding is the theoretical limit of compounding frequency. It uses the mathematical constant 'e' (approx. 2.718) to determine the maximum possible yield. In practice, the difference between daily and continuous compounding is less than 0.001% for most rates.
Strategy When should I compare APR instead of APY?
Use APR to compare the base cost of loans side by side. However, when evaluating the true cost of credit card debt (which compounds daily), calculate the APY — it will reveal the real annual cost, which is often significantly higher than the advertised APR.
Strategy Does a higher APY always mean a better investment?
Not necessarily. After accounting for fees, taxes, and inflation, a higher nominal APY may produce lower real returns. A 6% APY taxable account might yield less than a 5% APY in a tax-free Roth IRA for someone in a high tax bracket. Always compare real, after-tax yields.
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Formula & Methodology

Formula & Methodology

APR to APY

APY = (1 + r/n)^n − 1

Where r is the nominal APR as a decimal and n is the number of compounding periods per year. More frequent compounding produces a higher effective yield.

APY to APR

APR = n × ((1 + APY)^(1/n) − 1)

The reverse conversion extracts the nominal rate from a known effective yield and compounding frequency.

Real APY (Fisher Equation)

Real APY = ((1+APY)/(1+i)) − 1

Adjusts your nominal yield for inflation, revealing true purchasing power growth. i = inflation rate as decimal.

After-Tax APY

After-Tax APY = APY × (1 − τ)

Where τ is your marginal tax rate as a decimal. Use this to compare taxable vs. tax-advantaged accounts fairly.

Continuous Compounding

APY = e^r − 1

The theoretical maximum yield when compounding occurs at every instant. Uses Euler's number (e ≈ 2.71828).

Net APY (After Fees)

Net APY = (netFV/P)^(1/t) − 1

Where netFV equals gross future value minus the compounded value of all fees. Reveals the true yield on fee-bearing accounts.

About this calculation · Accuracy & Methodology

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Key Terms Explained

APR (Annual Percentage Rate) The nominal interest rate that does not account for intra-year compounding. Used to compare the base cost of loans.
APY (Annual Percentage Yield) The effective annual rate that includes compounding effects. Represents the actual return on savings or true cost of debt.
Real Rate The inflation-adjusted return. A 5% APY with 3% inflation gives a real rate of approximately 1.94%. This is your true gain in purchasing power.
Compounding Frequency How often interest is calculated and added to the balance: daily (365), monthly (12), quarterly (4), or annually (1).
Fee Drag The reduction in effective APY caused by account maintenance fees, origination fees, or management fees. Even small annual fees compound into significant losses over time.
Tax Drag The reduction in effective yield caused by income taxes on interest. Eliminated entirely in tax-advantaged accounts like Roth IRAs.
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Real-World Examples

👤

Alex

Example 1: HYSA Savings Account

Given: 4.5% APR, daily compounding, $10,000, 5 years, 3% inflation, 22% tax.

Gross APY: 4.603% | Real APY: 1.554% | After-Tax APY: 3.590% | Final Value: $12,526

APY by Compounding Frequency (5% APR)

FrequencyPeriods (n)APYExtra on $10k/yr
Annual15.000%$0.00
Semi-Annual25.063%$6.25
Quarterly45.095%$9.45
Monthly125.116%$11.62
Daily3655.127%$12.67
Continuous∞5.127%$12.71
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APR vs APY: What Every Saver and Borrower Should Know

Why Two Different Rates Exist

Financial institutions use APR and APY to describe interest from different perspectives. APR understates the true cost of borrowing because it ignores compounding, which benefits lenders. APY reveals the full picture by accounting for how frequently interest is calculated. Regulators require banks to disclose APY on savings products and APR on loans, but understanding both helps you make informed comparisons.

The Hidden Costs: Fees, Taxes, and Inflation

The advertised APY is just the starting point. Three forces silently erode your real returns: fees (account maintenance, origination costs), taxes (income tax on interest), and inflation (the general rise in prices). A savings account paying 5% APY sounds attractive, but after a 22% tax rate (leaving 3.9%), and 3% inflation (leaving ~0.87% real), your actual purchasing power gain is less than 1%. This calculator makes all three visible simultaneously.

Compounding: The Eighth Wonder

The gap between APR and APY grows with higher rates and more frequent compounding. At 5% with monthly compounding, the difference is modest (0.116%). But at 25% with daily compounding — typical of credit cards — the effective rate is 3.4 percentage points higher than the stated APR. This hidden cost is why credit card debt is so expensive. Conversely, for savings, maximizing compounding frequency is free money — switching from annual to daily compounding on a $100,000 deposit at 5% APR earns an extra $126.70 per year at no cost.

Practical Decision Framework

When comparing savings accounts, always compare APY — specifically after-tax real APY. When comparing loans, use APR for base cost, but calculate APY to understand the true annual cost. For mortgages, focus on the effective APR including all fees. For revolving credit, the difference between APR and APY is significant and costly. Use this calculator's Scenario Analysis tab to compare your rate against real market benchmarks, and the Wealth Projector to understand what every percentage point of APY means over 30 years.