Continuous Compounding
Worked example: $1000 at 5% continuous for 10 → A = 1648.72 — press Try an example to run it live, then adjust anything.
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Continuous Compounding explained
Continuous compounding is the limit of compounding ever more often — every instant, the balance grows in proportion to itself, giving . $5,000 at 4% per year for 10 years becomes 5000 × e⁰·⁴ ≈ $7,459.12, only a few dollars above monthly compounding: the compounding-frequency race hits a ceiling, and e is that ceiling.
The same law, with r negative, describes radioactive decay and drug elimination. Solving for t gives the exact doubling time t = ln 2 / r — at 4%, ln 2 / 0.04 ≈ 17.3 periods, which is where the banker's Rule of 72 comes from.
Continuous Compounding formula
- = Final amount
- = Principal
- = Interest rate per period (decimal)
- = Number of periods
Missing one of these? Work it out first, then come back
- Final amount — Exponential Growth, Exponential Decay
- Principal — Simple Interest, Compound Interest (Periodic)
- Interest rate per period (decimal) — Simple Interest, Compound Interest (Periodic)
- Number of periods — Exponential Growth, Exponential Decay