Compound interest calculator
Pick compounding frequency, read APY, and project a lump sum with optional monthly additions — year-by-year if you want the path.
Defaults to your region. Switch to compare any other scale.
USD defaults; pick compounding frequency freely.
Default 0. Added at month-end; for SIP-heavy plans prefer the investment calculator.
Result
$16,470.09
Future value
APY 5.12%
- Total contributed$10,000.00
- Interest earned$6,470.09
- Effective annual rate (APY)5.12%
- Horizon10
Illustration, not a bank quote
Nominal rate and compounding frequency determine APY. Taxes, fees, and variable rates are omitted. Continuous mode uses e^(rt) on the lump and monthly futureValue for contributions.
Year-by-year balance (first 10 years)
| Year | Balance | Contributed | Interest |
|---|---|---|---|
| 1 | $10,511.62 | $10,000.00 | $511.62 |
| 2 | $11,049.41 | $10,000.00 | $1,049.41 |
| 3 | $11,614.72 | $10,000.00 | $1,614.72 |
| 4 | $12,208.95 | $10,000.00 | $2,208.95 |
| 5 | $12,833.59 | $10,000.00 | $2,833.59 |
| 6 | $13,490.18 | $10,000.00 | $3,490.18 |
| 7 | $14,180.36 | $10,000.00 | $4,180.36 |
| 8 | $14,905.85 | $10,000.00 | $4,905.85 |
| 9 | $15,668.47 | $10,000.00 | $5,668.47 |
| 10 | $16,470.09 | $10,000.00 | $6,470.09 |
About this tool
Compound interest grows a balance by applying the rate to principal plus prior interest. Frequency matters: annual, semi-annual, quarterly, monthly, daily, or continuous compounding change the effective annual yield (APY) even when the nominal rate is fixed.
Enter starting principal, nominal annual rate, years, compounding frequency, and optional monthly contributions. The schedule shows how balances build year by year so you can compare frequencies side by side.
For SIP-style monthly investing with an investment framing, open the investment calculator. Retirement projections with a withdrawal check live on the retirement page. Outputs are illustrations, not advice.
Formula
Discrete: FV = P(1+r/n)^(n·t) + PMT × [((1+r/n)^(n·t) − 1) / (r/n)] (contrib mapped monthly)Continuous lump: A = P·e^(rt)APY = (1+r/n)^n − 1; continuous APY = e^r − 1
How it is calculated
- Enter principal, annual rate %, years, and compounding frequency.
- Optionally add a monthly contribution (default 0).
- We grow the lump at the chosen frequency (or e^(rt) if continuous) and add the monthly annuity when needed.
- APY / effective annual rate is shown from the nominal rate and frequency.
- If your country, school or provider uses different rules, pick another option in the “Standard” menu at the top.
Questions
What is APY / effective annual rate?
APY converts a nominal annual rate and compounding frequency into a single yearly yield: (1+r/n)^n − 1. Continuous compounding uses e^r − 1. It lets you compare accounts that compound at different paces.
How does continuous compounding treat monthly contributions?
The lump sum uses A = P·e^(rt). Any monthly contribution is added with the same monthly futureValue annuity used elsewhere (compoundsPerYear=12). Mixing continuous lump growth with a monthly annuity is a common planner approximation — stated here so you can compare with a pure discrete schedule.
How is this different from the investment calculator?
This page owns compounding frequency and APY (including continuous). The investment calculator is SIP / monthly-contribution focused with a fixed monthly compound path. Use both: frequency & APY here; SIP-style monthly plans there.
Does daily compounding use 365 or 360 days?
We use n = 365 for the daily option (common retail convention). Some money-market products use 360 — adjust mentally if your product states Actual/360.