Compound Interest Calculator
Understanding Compound Interest
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. It's essentially "interest on interest." This makes it a powerful tool for wealth growth over time, as your earnings start generating their own earnings.
How it Works:
The magic of compound interest lies in its exponential growth. Unlike simple interest, which is only calculated on the principal amount, compound interest reinvests your earnings. This means that each subsequent interest calculation is based on a larger sum – the original principal plus the accumulated interest.
The Formula:
The formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (as a decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
Key Factors Affecting Growth:
- Principal Amount: A larger initial investment will naturally grow to a larger sum.
- Interest Rate: Higher interest rates significantly accelerate growth.
- Time Horizon: The longer your money is invested, the more powerful compounding becomes. Even small differences in time can lead to substantial differences in the final amount.
- Compounding Frequency: More frequent compounding (e.g., daily vs. annually) generally leads to slightly higher returns, as interest is calculated and added to the principal more often, starting the "interest on interest" cycle sooner.
Example Calculation:
Let's say you invest $1,000 (P) at an annual interest rate of 5% (r = 0.05) for 10 years (t), compounded monthly (n = 12).
A = 1000 * (1 + 0.05/12)^(12*10)
A = 1000 * (1 + 0.00416667)^(120)
A = 1000 * (1.00416667)^(120)
A = 1000 * 1.647009
A ≈ $1,647.01
After 10 years, your initial $1,000 investment would grow to approximately $1,647.01, with $647.01 being the accumulated compound interest.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var time = parseFloat(document.getElementById("time").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || isNaN(annualRate) || isNaN(time) || isNaN(compoundingFrequency) ||
principal < 0 || annualRate < 0 || time < 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = time * compoundingFrequency;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
var totalInterest = futureValue – principal;
resultDiv.innerHTML =
"
Initial Investment: $" + principal.toFixed(2) + "" +
"
Annual Interest Rate: " + annualRate.toFixed(2) + "%" +
"
Time Period: " + time + " years" +
"
Compounding Frequency: " + getCompoundingFrequencyText(compoundingFrequency) + "" +
"
Total Accumulated Amount: $" + futureValue.toFixed(2) + "" +
"
Total Compound Interest Earned: $" + totalInterest.toFixed(2) + "";
}
function getCompoundingFrequencyText(frequency) {
switch (frequency) {
case 1: return "Annually";
case 2: return "Semi-Annually";
case 4: return "Quarterly";
case 12: return "Monthly";
case 365: return "Daily";
default: return "Custom";
}
}
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font-family: sans-serif;
max-width: 800px;
margin: 20px auto;
padding: 20px;
border: 1px solid #e0e0e0;
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flex-direction: column;
}
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margin-bottom: 5px;
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}
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background-color: #0056b3;
}
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}
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}
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