Compound Interest Calculator
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." This means that your money grows at an accelerated rate over time compared to simple interest, where interest is only calculated on the original principal amount.
How Compound Interest Works
The power of compound interest lies in the fact that your earnings begin to generate their own earnings. Over time, this snowball effect can significantly boost your investment growth. The key factors influencing compound interest are:
- Principal Amount: The initial sum of money you invest or deposit. A larger principal will result in greater overall interest earned.
- Annual Interest Rate: The percentage at which your investment grows each year. Higher rates lead to faster growth.
- Time Period: The longer your money is invested, the more time it has to compound and grow. Even small amounts can become substantial over many years.
- Compounding Frequency: How often the interest is calculated and added to the principal. More frequent compounding (e.g., daily vs. annually) generally leads to slightly higher returns due to interest being calculated on previously earned interest more often.
The formula used to calculate 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
Example Calculation
Let's consider an example. If you invest $1,000 (P) at an annual interest rate of 5% (r = 0.05), compounded monthly (n = 12), for 10 years (t):
- 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
In this scenario, your initial $1,000 would grow to approximately $1,647.01 after 10 years, meaning you would have earned about $647.01 in compound interest.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var years = parseFloat(document.getElementById("years").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
if (isNaN(principal) || isNaN(annualRate) || isNaN(years) || isNaN(compoundingFrequency) || principal < 0 || annualRate < 0 || years < 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = years * compoundingFrequency;
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) + "%" +
"
Investment Period: " + years + " years" +
"
Compounding Frequency: " + getFrequencyName(compoundingFrequency) + "" +
"
Total Future Value: $" + futureValue.toFixed(2) + "" +
"
Total Compound Interest Earned: $" + totalInterestEarned.toFixed(2) + "";
}
function getFrequencyName(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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