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." Daily compounding means this interest is calculated and added to the principal every single day.
The Formula for Daily Compound Interest
The formula to calculate the future value (FV) of an investment with daily compounding is:
FV = P * (1 + r/n)^(nt)
Where:
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 = Time the money is invested or borrowed for, in years
For daily compounding, the number of compounding periods per year (n) is typically 365 (or 360 in some financial contexts, but 365 is more common for daily calculations).
To find just the interest earned, you can use this formula:
Interest Earned = FV - P
How the Calculator Works
Our calculator simplifies this process. It takes:
Principal Amount: The initial sum of money you are investing or borrowing.
Annual Interest Rate: The yearly rate of return, expressed as a percentage.
Time (Years): The duration for which the money is invested or borrowed.
The calculator then applies the daily compounding formula. It converts the annual rate to a daily rate (Annual Rate / 365) and calculates the total number of compounding periods (Time in Years * 365). This allows for precise calculation of how your money can grow over time due to the frequent addition of interest.
Why Daily Compounding Matters
The more frequently interest is compounded, the faster your investment will grow (or the more you'll owe on a loan). Daily compounding offers a significant advantage over monthly or annual compounding because it allows interest to start earning interest sooner, leading to a higher effective yield over time. This is particularly beneficial for long-term investments and savings accounts.
Use Cases
Investment Growth: Project how much your savings or investments will grow over several years.
Loan Interest: Estimate the total interest you'll pay on a loan with daily compounding, although many loans compound less frequently.
Financial Planning: Understand the power of consistent saving and the benefits of higher compounding frequencies.
function calculateCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var timeYears = parseFloat(document.getElementById("timeYears").value);
if (isNaN(principal) || principal <= 0) {
alert("Please enter a valid principal amount greater than zero.");
return;
}
if (isNaN(annualRate) || annualRate < 0) {
alert("Please enter a valid annual interest rate.");
return;
}
if (isNaN(timeYears) || timeYears <= 0) {
alert("Please enter a valid time in years greater than zero.");
return;
}
var dailyRate = annualRate / 100 / 365;
var numberOfPeriods = timeYears * 365;
// Calculate Future Value
// FV = P * (1 + r/n)^(nt)
var futureValue = principal * Math.pow(1 + dailyRate, numberOfPeriods);
// Calculate total interest earned
var interestEarned = futureValue – principal;
// Display the result
document.getElementById("result").innerHTML = "Your total interest earned will be: $" + interestEarned.toFixed(2) + "";
}