Calculate the future value of an investment with compound interest.
Understanding Compound Interest
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. In essence, it's "interest on interest." This makes it a powerful tool for wealth building over time, as your money grows at an accelerating rate.
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
Understanding how each component affects your investment is crucial. A higher principal, a higher interest rate, a longer time period, and more frequent compounding all contribute to a greater future value.
Example Calculation:
Let's say you invest $10,000 (Principal) at an 8% annual interest rate (0.08 as a decimal) for 20 years. If the interest is compounded annually (n=1), the calculation would be:
A = 10000 * (1 + 0.08/1)^(1*20)
A = 10000 * (1.08)^20
A = 10000 * 4.660957…
A ≈ $46,610
Now, consider the same investment but compounded monthly (n=12):
A = 10000 * (1 + 0.08/12)^(12*20)
A = 10000 * (1 + 0.006666…)^(240)
A = 10000 * (1.006666…)^240
A = 10000 * 4.926803…
A ≈ $49,268
As you can see, compounding monthly yields a higher return due to the increased frequency of interest being added to the principal.
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");
// Input validation
if (isNaN(principal) || principal <= 0) {
resultDiv.innerHTML = "Please enter a valid principal amount greater than zero.";
return;
}
if (isNaN(annualRate) || annualRate < 0) {
resultDiv.innerHTML = "Please enter a valid annual interest rate (can be zero or positive).";
return;
}
if (isNaN(time) || time <= 0) {
resultDiv.innerHTML = "Please enter a valid time period in years greater than zero.";
return;
}
if (isNaN(compoundingFrequency) || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter a valid compounding frequency greater than zero.";
return;
}
var ratePerPeriod = annualRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * time;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
// Format the result to two decimal places for currency
var formattedFutureValue = futureValue.toFixed(2);
var totalInterestEarned = (futureValue – principal).toFixed(2);
resultDiv.innerHTML = "