Compound Interest Calculator
See how your money grows over time with the power of compound interest. Enter your starting amount, interest rate, compounding frequency, and optional monthly contributions to get a full year-by-year breakdown.
How Compound Interest Works
The Compound Interest Formula
For a lump sum with no additional contributions:
A = P × (1 + r/n)^(n×t)
With regular contributions added each period:
A = P×(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) − 1) / (r/n)]
P = principal r = annual rate n = compounds per year t = years PMT = periodic contribution
Worked Example — $10,000 at 7% Monthly for 20 Years + $200/month
- Monthly rate r/n = 7% ÷ 12 = 0.5833%
- Periods n×t = 12 × 20 = 240
- Lump-sum FV = 10,000 × (1.005833)^240 = $40,064
- Contribution FV = 200 × [(1.005833^240 − 1) / 0.005833] = $104,185
- Total FV = $40,064 + $104,185 = $144,249
- Total contributed = $10,000 + $200 × 240 = $58,000
- Interest earned = $144,249 − $58,000 = $86,249
Effect of Compounding Frequency — $10,000 at 7% for 10 Years
| Frequency | Times/Year | Future Value | Effective Annual Rate |
|---|---|---|---|
| Annually | 1 | $19,672 | 7.000% |
| Semi-Annually | 2 | $19,799 | 7.123% |
| Quarterly | 4 | $19,865 | 7.186% |
| Monthly | 12 | $20,097 | 7.229% |
| Daily | 365 | $20,137 | 7.250% |
| Continuously | ∞ | $20,138 | 7.251% |
Rule of 72 — Quick Doubling Time Reference
| Annual Rate | Years to Double (Rule of 72) | Exact Years |
|---|---|---|
| 2% | 36.0 years | 35.0 years |
| 3% | 24.0 years | 23.4 years |
| 4% | 18.0 years | 17.7 years |
| 5% | 14.4 years | 14.2 years |
| 6% | 12.0 years | 11.9 years |
| 7% | 10.3 years | 10.2 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
2025 US Savings & Investment Rate Benchmarks
| Account / Vehicle | Institution | Typical Rate | Compounds |
|---|---|---|---|
| High-Yield Savings | Marcus (Goldman Sachs) | 4.50% APY | Daily |
| High-Yield Savings | Ally Bank | 4.35% APY | Daily |
| High-Yield Savings | SoFi | 4.60% APY | Daily |
| High-Yield Savings | Discover Bank | 4.25% APY | Daily |
| 1-Year CD | Synchrony Bank | 5.00% APY | Daily |
| 5-Year CD | Ally Bank | 4.00% APY | Daily |
| Money Market | Vanguard Federal MM | 5.25% (7-day yield) | Daily |
| S&P 500 Index Fund | Historical average | ~10% nominal / ~7% real | Annual |
| US Total Stock Market ETF | Vanguard (VTI) | ~10.2% (30-yr avg) | Annual |
| US Treasury Bills (1-yr) | TreasuryDirect | ~4.90% (Jan 2025) | At maturity |
Rates as of January 2025 — subject to change; verify with institution.
Simple vs Compound Interest Comparison — $5,000 at 8% for 30 Years
| Type | 10 Years | 20 Years | 30 Years |
|---|---|---|---|
| Simple Interest | $9,000 | $13,000 | $17,000 |
| Compound (Annual) | $10,795 | $23,305 | $50,313 |
| Compound (Monthly) | $11,102 | $24,647 | $54,914 |
| Compound (Daily) | $11,127 | $24,751 | $55,280 |
References
- Federal Reserve — H.15 Selected Interest Rates release (deposit rates).
- FDIC — National rates and rate caps for savings deposits.
- Internal Revenue Service (IRS) — Publication 550, Investment Income and Expenses.
- Vanguard Research — Historical equity returns and long-term compounding data.
- Ibbotson & Sinquefield — Stocks, Bonds, Bills and Inflation (SBBI) Yearbook.
