APY Calculator
Calculate your true Annual Percentage Yield (APY), compare compound interest frequencies, convert APR to APY, and project future investment growth.
| Financial Component | Value | % Share / Rate |
|---|---|---|
| Stated Interest Rate (Nominal APR) | Base Rate | 5.000% |
| Annual Percentage Yield (APY) | Monthly (12x) | 5.116% |
| Initial Principal Deposit | $10,000.00 | 50.93% |
| Total Additional Contributions | $6,000.00 | 30.56% |
| Total Compound Interest Earned | $3,634.20 | 18.51% |
| Ending Balance (Future Value) | $19,634.20 | 100.00% |
* Results are estimates for educational and planning purposes only and do not constitute formal financial, tax, or investment advice.
| Year | Annual Deposits | Interest Earned | Total Deposits to Date | Total Interest to Date | Ending Balance |
|---|---|---|---|---|---|
| Year 1 | $1,200.00 | $539.50 | $11,200.00 | $539.50 | $11,739.50 |
| Year 2 | $1,200.00 | $628.50 | $12,400.00 | $1,168.01 | $13,568.01 |
| Year 3 | $1,200.00 | $722.05 | $13,600.00 | $1,890.06 | $15,490.06 |
| Year 4 | $1,200.00 | $820.39 | $14,800.00 | $2,710.44 | $17,510.44 |
| Year 5 | $1,200.00 | $923.75 | $16,000.00 | $3,634.20 | $19,634.20 |
Understanding APY: The Effective Power of Compounding
The Annual Percentage Yield (APY) reflects the true annual rate of return earned on a deposit, factoring in the effect of compound interest. Under the federal Truth in Savings Act (Regulation DD), financial institutions are legally required to disclose APY on deposit products (such as high-yield savings accounts, money market accounts, and certificates of deposit) so consumers can directly compare returns across different compounding schedules.
Mathematical Formulation
For discrete compounding frequencies, APY is calculated using the standard actuarial formula:
APY = [ 1 + (r / n) ]n − 1
Where r represents the stated nominal annual interest rate (as a decimal) and n represents the number of compounding periods per calendar year.
When interest compounds continuously, the formula transitions to its natural exponential limit:
APYcontinuous = er − 1
To reverse-engineer the nominal interest rate from a known APY, use:
r = n × [ (1 + APY)1/n − 1 ]
Compounding Frequency Benchmark Comparison
The table below illustrates the impact of compounding frequencies on a $10,000 deposit earning a 5.00% nominal interest rate over 1 and 5 years:
| Compounding Schedule | Periods / Year (n) | Effective APY | 1-Year Interest | 5-Year Balance |
|---|---|---|---|---|
| Annually | 1 | 5.000% | $500.00 | $12,762.82 |
| Semi-Annually | 2 | 5.063% | $506.25 | $12,800.85 |
| Quarterly | 4 | 5.095% | $509.45 | $12,820.37 |
| Monthly | 12 | 5.116% | $511.62 | $12,833.59 |
| Bi-Weekly | 26 | 5.122% | $512.23 | $12,837.36 |
| Daily | 365 | 5.127% | $512.67 | $12,840.03 |
| Continuous | ∞ | 5.127% | $512.71 | $12,840.25 |
How to Use This Calculator
- Select Calculation Mode: Choose "Interest Rate to APY" to calculate yield and future balance, "APY to Interest Rate" to find the base rate, or "Compounding Frequency Matrix" to view all schedules side by side.
- Input Financial Parameters: Enter your initial balance, stated annual interest rate, compounding schedule, and optional recurring deposits.
- Review Key Metrics & Charts: Inspect your effective APY, compounding yield bonus, 2D balance allocation donut, and annual growth breakdown.
- Export Summary: Click "Copy" to save a formatted summary to your clipboard, or "Print" to create a PDF record.