Continuously Compounded Interest Calculator: Maximize Your Investment Growth
Enter your principal, contribution plan and two interest rates, press “Calculate,” and the script returns future value using continuous-compounding math. Continuous interest applied at 10 % grows $10,000 to about $18,221 in six years (NerdWallet, 2024).
Compound Interest Calculator
Future Value:
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How to use the tool
Initial Principal ($)
• Example 1: 18,500 • Example 2: 27,750
Initial Interest Rate (%)
• Example 1: 6.2 • Example 2: 8.4
Number of Yearly Contributions
• Example 1: 12 • Example 2: 25
Yearly Contribution Amount ($)
• Example 1: 2,750 • Example 2: 5,600
Subsequent Interest Rate (%)
• Example 1: 5.0 • Example 2: 6.8
Press “Calculate.” The future value appears instantly.
Underlying formulas
The calculator applies continuous compounding to both the starting lump sum and each yearly deposit:
$$
A = P\,e^{r t} + \sum_{i=1}^{t} C\,e^{s i}
$$
P = initial principal
C = annual contribution
r = initial rate (decimal)
s = subsequent rate (decimal)
t = total years
Worked example
Inputs: P = 20,000; r = 6 %; C = 3,000; s = 5 %; t = 12 years.
Lump-sum growth: 20,000 × e0.06 × 12 ≈ 41,088.66
Deposit growth: 3,000 × ∑i=1…12e0.05 i ≈ 50,678.90
Future value: 41,088.66 + 50,678.90 ≈ 91,767.56
Quick-Facts
Continuous compounding uses Euler’s number 2.71828 (NIST Digital Library of Mathematical Functions, 2023).
Formula maximises growth by treating interest as added every instant (Investopedia, 2024).
Real-world high-yield savings average 4–5 % APY in 2024 (FDIC Weekly Rates, 2024).
IRAs allow ≤ 6,500 USD yearly contribution for those < 50 yr (IRS Pub 590-A, 2024).
FAQ
What is continuous compound interest?
Continuous compounding applies interest an infinite number of times per period, producing $$A=P\,e^{rt}$$ where e≈2.71828 (NIST, 2023). This yields the maximum possible growth for a fixed nominal rate.
Why does the form ask for two rates?
Your initial deposit may earn a promotional rate while later deposits earn the prevailing rate. Distinct fields let you model both scenarios accurately (Federal Reserve Consumer Guide, 2023).
Can I change contribution frequency?
This version assumes yearly deposits. To model monthly deposits, divide the annual amount by 12 and set contributions to the total number of months—then convert rates to monthly decimals.
How accurate is the result?
The math is exact, but taxes, fees and inflation alter real returns. U.S. inflation averaged 3.2 % in 2023 (BLS CPI Summary, 2024), reducing purchasing power.
Does continuous compounding really exist in banking?
Banks calculate interest daily or monthly. Continuous compounding is a theoretical upper bound, useful for modelling and pricing derivatives (Hull, Options & Futures, 2022).
How do I get the decimal rate?
Divide the percentage by 100. For 6.8 %, use 0.068.
What is Euler’s number?
Euler’s number e is the limit of (1 + 1/n)n as n→∞ and underpins continuous growth phenomena (Courant, Differential Calculus, 2021).
Is this tool suitable for debt modelling?
Yes. Enter a negative yearly contribution to represent payments and a positive rate to see how fast debt shrinks or grows.
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