Understanding Compound Interest
Compound interest is often referred to as "interest on interest." Unlike simple interest, which is calculated only on the principal amount, compound interest allows your earnings to grow exponentially over time. The more frequently your interest is compounded, the faster your investment will grow.
The Formula:
The formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interestP = 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 yeart = the number of years the money is invested or borrowed for
Example:
Let's say you invest $1,000 (P) at 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 $1,000 investment would grow to approximately $1,647.01 after 10 years due to the power of compounding.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var compoundingPeriods = parseFloat(document.getElementById("compoundingPeriods").value);
var years = parseFloat(document.getElementById("years").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(principal) || isNaN(annualRate) || isNaN(compoundingPeriods) || isNaN(years) ||
principal <= 0 || annualRate <= 0 || compoundingPeriods <= 0 || years <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingPeriods;
var totalPeriods = compoundingPeriods * years;
var futureValue = principal * Math.pow(1 + ratePerPeriod, totalPeriods);
resultDiv.innerHTML = "
Results
" +
"Your initial investment of $" + principal.toFixed(2) + " will grow to approximately $" + futureValue.toFixed(2) + " after " + years + " years." +
"Total interest earned: $" + (futureValue – principal).toFixed(2) + "";
}
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