Continuous Compound Interest Calculator
Project your investment growth and plan for financial goals with this calculator. Continuous compounding calculates interest accumulated constantly, maximizing growth potential.
Understanding Your Projections
- Starting Balance: Your initial investment amount
- Regular Contributions: How much you add periodically
- Growth Rate: Expected annual return on investments
- Time Horizon: Years until you need the money
Factors That Affect Growth
1. Compounding Frequency: More frequent compounding slightly increases returns 2. Contribution Timing: Earlier contributions have more time to grow 3. Rate of Return: Even small rate differences compound significantly over time 4. Time: The most powerful factor in wealth building
Tax Considerations
Different account types have different tax treatment:
- Tax-Deferred (Traditional IRA, 401k): Pay taxes on withdrawal
- Tax-Free (Roth IRA, HSA): Pay taxes upfront, growth is tax-free
- Taxable: Pay taxes annually on dividends and when selling
Continuous Compounding
Continuous compounding is the mathematical limit as the number of periods goes to infinity:
``
A = Pe^(rt)
`
It is not a product anyone sells — no bank compounds continuously — but it is the standard
convention in options pricing and academic finance, where it makes the maths tractable.
The practical point is how little it buys. At 5%, continuous compounding gives 5.127% APY;
daily gives 5.127% as well, to three decimal places. Continuous compounding is the ceiling,
and daily compounding has already reached it for any purpose involving actual money.
The Two Things That Actually Move the Number
Over a long horizon, contribution amount and time in the market dominate the rate. $500 a
month at 7% for 30 years reaches about $566,000; the same money at 8% reaches $679,000, but
starting five years later at 8% reaches only $442,000.
| Change | Effect over 30 years on $500/month |
|---|---|
| +1% return | +$113,000 |
| +$100/month | +$113,000 |
| Starting 5 years earlier | +$237,000 |
Starting earlier is worth more than either, and it is the only one of the three you cannot
buy back later.The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
| Year | Deposited | Balance | Growth | Growth on deposits |
|---|---|---|---|---|
| 1 | $12,400 | $13,201 | $801 | 6% |
| 5 | $22,000 | $28,495 | $6,495 | 30% |
| 10 | $34,000 | $54,714 | $20,714 | 61% |
| 20 | $58,000 | $144,573 | $86,573 | 149% |
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
`
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
``
The second term usually dominates. On these numbers the $200 monthly contribution accounts for the larger share of the final balance, which is the practical lesson: how much you add matters more than the rate, right up until the balance gets large.