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. It's often referred to as "interest on interest," and it's a powerful force in wealth building over time.
How Compound Interest Works
Unlike simple interest, which is only calculated on the principal amount, compound interest grows exponentially. Each time interest is compounded, it's added to the principal, and then the next interest calculation is based on this new, larger sum. This effect accelerates your investment growth significantly, especially over longer periods.
The Compound Interest Formula
The formula for compound interest is:
A = P (1 + r/n)^(nt)
- 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
Example Calculation
Let's say you invest $1,000 (P) with an annual interest rate of 5% (r = 0.05), compounded monthly (n = 12), for 10 years (t).
Using the formula:
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
This means your initial investment of $1,000 would grow to approximately $1,647.01 after 10 years, with $647.01 being the accumulated compound interest.
Why Compounding Matters
The key takeaway is that the sooner you start investing and the longer you let your money compound, the more significant the growth will be. Even small amounts invested regularly can accumulate substantial wealth over decades due to the power of compounding.
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 = parseFloat(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(principal) || isNaN(annualRate) || isNaN(time) || isNaN(compoundingFrequency)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (principal <= 0 || annualRate < 0 || time <= 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter positive values for principal, time, and compounding frequency, and a non-negative interest rate.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * time;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
var totalInterestEarned = futureValue – principal;
resultDiv.innerHTML =
"
Initial Investment: $" + principal.toFixed(2) + "" +
"
Annual Interest Rate: " + annualRate.toFixed(2) + "%" +
"
Time Period: " + time + " years" +
"
Compounding Frequency: " + compoundingFrequency + " times per year" +
"
Total Amount (Principal + Interest): $" + futureValue.toFixed(2) + "" +
"
Total Interest Earned: $" + totalInterestEarned.toFixed(2) + "";
}
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font-family: Arial, sans-serif;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
background-color: #f9f9f9;
}
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text-align: center;
margin-bottom: 20px;
color: #333;
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