Compound Interest Calculator
Understanding Compound Interest
Compound interest is often called "interest on interest." It's a powerful concept in finance that allows your money to grow exponentially over time. Unlike simple interest, which is calculated only on the initial principal amount, compound interest is calculated on the principal amount plus any interest that has already been accumulated.
How It Works:
Imagine you invest $1,000 at an annual interest rate of 5%, compounded annually. After the first year, you'd earn $50 in interest (5% of $1,000). Your new balance is $1,050. In the second year, you earn 5% interest on $1,050, which is $52.50. Your balance grows to $1,102.50. This might seem small initially, but over many years, the effect becomes significant.
Key Factors:
- Principal Amount: The initial sum of money invested or borrowed. A larger principal will lead to greater overall growth.
- Annual Interest Rate: The percentage of interest earned or paid per year. Higher rates lead to faster growth.
- Number of Years: The longer your money is invested, the more time it has to compound and grow. Time is one of the most crucial elements of compounding.
- Compounding Frequency: How often the interest is calculated and added to the principal. The more frequent the compounding (e.g., daily vs. annually), the faster your money will grow, as interest starts earning interest sooner.
The Formula:
The compound interest formula 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 Scenario:
Let's say you invest $5,000 (P) at an annual interest rate of 7% (r = 0.07), compounded quarterly (n = 4), for 15 years (t). Using the formula:
A = 5000 * (1 + 0.07/4)^(4*15)
A = 5000 * (1 + 0.0175)^(60)
A = 5000 * (1.0175)^60
A = 5000 * 2.8194
A ≈ $14,097.00
So, your initial $5,000 investment would grow to approximately $14,097.00 after 15 years.
This calculator helps you visualize how different variables can impact your investment's growth through the power of compounding.
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");
resultDiv.innerHTML = ""; // Clear previous results
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;
var formattedFutureValue = futureValue.toFixed(2);
var formattedTotalInterest = totalInterestEarned.toFixed(2);
resultDiv.innerHTML = `
Calculation Results:
Initial Investment: $${principal.toFixed(2)}
Annual Interest Rate: ${annualRate.toFixed(2)}%
Investment Duration: ${years} years
Compounding Frequency: ${getCompoundingFrequencyText(compoundingFrequency)}
Total Interest Earned: $${formattedTotalInterest}
Total Future Value: $${formattedFutureValue}
`;
}
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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}
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