How to Use This APR vs APY Calculator
Our calculator simulates complex compounding calculations in a few clicks. Follow these steps to map your retirement projections:
- Input Initial Investment: Set the capital you start with. Slide the range or type in any number up to $10,000,000.
- Define Interest Rate: Enter your expected annual yield. You can click on presets like historical S&P 500 CAGR (10.7%) or High-Yield Savings rates (4.8%).
- Select Frequency & Timeframe: Decide whether your interest compounds daily, monthly, quarterly, or annually. Then define your timeline in either years or months.
- Add Periodic Contributions: If you plan to make monthly, quarterly, or annual additions, input the amount and timing (beginning or end of period) to compound your growth rate.
Understanding Compound Interest
Compound interest is the math of adding interest back to the principal sum so that interest is earned on interest. This creates an exponential growth curve that accelerates your money's value as time passes. It differs from simple interest, which is calculated solely on the initial principal and does not grow exponentially.
For long-term savers, compounding is the ultimate tool. Small monthly additions combined with early compounding periods can easily result in interest earnings representing 80%+ of your final portfolio balances.
The Compound Interest Formula
The APR-to-APY conversion uses the standard compound interest formula to find the true annual yield, accounting for how often interest is added within the year:
Formula Variable Guide
| APY | Annual Percentage Yield — the effective annual return after compounding |
| APR | Annual Percentage Rate — the nominal (stated) rate |
| n | Number of compounding periods per year (12 = monthly, 365 = daily) |
Why Compounding Matters
To highlight the impact of compounding frequency, here's how a 5% APR translates to APY for different products:
| Product | Compounding | APY | vs APR |
|---|---|---|---|
| Simple interest loan | Annual | 5.000% | 0% |
| Bond (semi-annual) | Semi-Annual | 5.063% | +0.063% |
| Savings account | Quarterly | 5.095% | +0.095% |
| High-yield savings | Monthly | 5.116% | +0.116% |
| Daily-compounding account | Daily | 5.127% | +0.127% |
APR vs. APY: The Numbers Behind the Marketing
Why banks use different rates for loans vs. savings — and what it actually costs you.
APR vs. APY Across Real Financial Products
The same compounding math that grows investments works against you on debt. Here's how APR and APY diverge across common financial products:
| Product Type | Advertised Rate | Type Advertised | Actual APY | Difference |
|---|---|---|---|---|
| High-Yield Savings Account | 5.00% | APY | 5.00% | — (already APY) |
| Standard Credit Card | 22.99% | APR | 25.84% | +2.85% |
| Mortgage (30-yr fixed) | 7.00% | APR | 7.23% | +0.23% |
| Auto Loan | 8.50% | APR | 8.84% | +0.34% |
| Crypto Lending Platform | 12.00% | APY | 12.00% | — (already APY) |
| Store Credit Card | 29.99% | APR | 34.96% | +4.97% |
On savings, APY is advertised because it is a higher, more attractive number. On loans, APR is advertised because it understates the compounding costs, looking cheaper.
Why Lenders Understate Cost of Credit: The Practical Implication
Lenders are required by law to disclose APR — but APR understates the true cost of credit because it doesn't account for compounding.
How Much Does Compounding Frequency Actually Change the APY?
Starting with a 5.00% APR, here's what you actually earn or pay depending on compounding frequency:
| Compounding Frequency | Effective APY | Annual Earnings on $10,000 |
|---|---|---|
| Annually | 5.000% | $500.00 |
| Semi-annually | 5.063% | $506.25 |
| Quarterly | 5.095% | $509.45 |
| Monthly | 5.116% | $511.62 |
| Daily | 5.127% | $512.67 |
| Continuously | 5.127% | $512.71 |
The difference between annual and daily compounding on $10,000 is $12.67/yr. However, on $500,000 over 20 years, daily vs. annual compounding produces a gap of roughly $32,400.
Why Crypto APY Is Not the Same as Savings Account APY — A Practical Warning
| Platform Type | Typical APY Range | Capital Safety | Regulated? |
|---|---|---|---|
| FDIC-insured HYSA | 4–5.5% | Very High | Yes |
| US Treasury Bills | 4.5–5.3% | Highest | Yes |
| Money Market Fund | 4.5–5.2% | High | Yes (SEC) |
| Crypto CeFi (e.g. Coinbase) | 3–6% | Medium | Partial |
| DeFi Stablecoin Yield | 5–15% | Low–Medium | No |
| DeFi Token Yield | 20–200%+ | Very Low | No |