Understanding Compound Interest
Compound interest is the interest on a savings account or loan that is calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a specific date. This is also referred to as "interest on interest," a concept that makes the investment grow at a faster rate than simple interest over time.
How it Works:
Imagine you invest $1,000 at an annual interest rate of 5%, compounded annually. After the first year, you'll earn $50 in interest ($1,000 * 0.05), bringing your total to $1,050. In the second year, you'll earn interest not just on the original $1,000, but also on the $50 interest from the first year. This means you'll earn $52.50 in interest ($1,050 * 0.05), and your total will grow to $1,102.50. This accelerating growth is the power of compounding.
The Formula:
The future value (FV) of an investment using compound interest can be calculated with the following formula:
FV = P (1 + r/n)^(nt)
- FV: Future Value of the investment/loan, including interest
- P: Principal amount (the initial amount of money)
- r: Annual interest rate (as a decimal)
- n: Number of times that interest is compounded per year
- t: Number of years the money is invested or borrowed for
Key Factors Influencing Growth:
- Principal Amount: A larger initial investment will yield higher returns over time.
- Interest Rate: Higher interest rates lead to faster growth.
- Time Period: The longer your money is invested, the more significant the effect of compounding.
- Compounding Frequency: More frequent compounding (e.g., daily vs. annually) generally leads to slightly higher returns due to interest being added and earning interest more often.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var timePeriod = parseFloat(document.getElementById("timePeriod").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(principal) || isNaN(annualInterestRate) || isNaN(timePeriod) || isNaN(compoundingFrequency)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (principal <= 0 || annualInterestRate < 0 || timePeriod <= 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = "Please enter positive values for principal, time, and compounding frequency, and a non-negative interest rate.";
return;
}
var ratePerPeriod = annualInterestRate / 100 / compoundingFrequency;
var numberOfPeriods = compoundingFrequency * timePeriod;
var futureValue = principal * Math.pow((1 + ratePerPeriod), numberOfPeriods);
// Format the results for better readability
var formattedFutureValue = futureValue.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 });
var formattedPrincipal = principal.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 });
var formattedInterestEarned = (futureValue – principal).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 });
resultDiv.innerHTML =
"
Principal Amount: $" + formattedPrincipal + "" +
"
Annual Interest Rate: " + annualInterestRate + "%" +
"
Time Period: " + timePeriod + " years" +
"
Compounding Frequency: " + getCompoundingFrequencyText(compoundingFrequency) + "" +
"
Total Interest Earned: $" + formattedInterestEarned + "" +
"
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";
}
}