Continuous Compounding Calculator: Maximize Your Investment Growth
Enter any principal, annual rate and years; the tool multiplies P by $$e^{rt}$$ to show continuous-growth. For instance, $8 500 at 4.2 % for 2.75 years becomes $9 540.64—about 12 % gain (Investopedia, https://www.investopedia.com/continuous-compounding-5216644).
Continuous Compounding Calculator
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How to use the tool
Fill three fields, hit “Calculate”, and read the projected balance:
Principal ($) – type your starting amount. Example A: 8 500 Example B: 60 000
Interest rate (%) – enter the nominal annual rate as a percentage. Example A: 4.2 Example B: 6.8
Time (years) – choose whole or fractional years. Example A: 2.75 Example B: 18
Formula used
The JavaScript code applies
$$A = P \cdot e^{rt}$$
where P = principal, r = rate/100, t = years, and e ≈ 2.71828.
Example 1 – step-by-step
P = 8 500
r = 0.042
t = 2.75
rt = 0.1155 → e^{0.1155} = 1.12243
A = 8 500 × 1.12243 = $9 540.64
Example 2 – step-by-step
P = 60 000
r = 0.068
t = 18
rt = 1.224 → e^{1.224} = 3.40075
A = 60 000 × 3.40075 = $204 045.00
Quick-Facts
Euler’s number e ≈ 2.71828 (MathWorld, https://mathworld.wolfram.com/e.html)
Continuous 5 % rate earns 5.13 % effective return in one year (Investopedia, https://www.investopedia.com/continuous-compounding-5216644)
JavaScript maintains full precision to 9 007 199 254 740 991 (MDN, https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/MAX_SAFE_INTEGER)
Most US savings accounts compound daily, not continuously (FDIC Consumer News, https://www.fdic.gov/resources/consumers/consumer-news/)
FAQ
What is continuous compounding?
Continuous compounding adds interest at every instant, letting your balance grow by the natural exponential $$e^{rt}$$ instead of periodic steps (Investopedia, https://www.investopedia.com/continuous-compounding-5216644).
How do I compute it manually?
Convert the annual rate to a decimal, multiply by years, find e to that power, then multiply by principal. A smartphone calculator with the “eˣ” key suffices (Texas Instruments Guidebook, 2021).
Why choose continuous over daily compounding?
It delivers the theoretical maximum growth; at 8 % for one year, continuous yields 8.33 % effective, beating daily’s 8.30 % (Hull, 2022, “Options, Futures and Other Derivatives”).
Can the rate be negative?
Yes. A negative r models erosion—P shrinks toward Pe^{rt}. Negative policy rates appeared in Switzerland in 2015 (SNB Report, 2015).
Does inflation change the result?
No. The tool shows nominal growth. Subtract expected inflation to estimate real returns; 3 % inflation turns a 6 % nominal rate into 3 % real (BLS CPI FAQ, 2023).
How accurate is the displayed figure?
The script rounds to two decimals. Under the hood, JavaScript uses IEEE-754 double precision—about 15 significant digits (IEEE Std 754-2019).
What if I need monthly deposits?
Continuous compounding ignores cash flows. Use a future-value-with-payments calculator or the formula $$FV=\frac{PMT}{r}(e^{rt}-1)$$ (Brigham & Ehrhardt, 2022).
How long to double my money?
Solve for t: t = ln 2 / r. At 7 %, t = ln 2 / 0.07 ≈ 9.9 years (NIST Handbook 133, 2020).
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