Daily compounded interest is a powerful concept in finance where interest is calculated and added to the principal amount on a daily basis. This means that not only does your initial investment earn interest, but the interest earned each day also begins to earn interest, creating a snowball effect known as compounding. This phenomenon, often referred to as "interest on interest," can significantly boost the growth of your investments or the cost of your debt over time compared to less frequent compounding periods (like monthly or annually).
The Formula for Daily Compounded Interest
The standard formula for calculating the future value (FV) of an investment with daily compounding is:
FV = P (1 + r/n)^(nt)
Where:
FV is the future value of the investment/loan, including interest.
P is the principal investment amount (the initial deposit or loan amount).
r is the annual interest rate (as a decimal).
n is the number of times that interest is compounded per year. For daily compounding, n = 365 (or 360 in some financial contexts, though 365 is more common for general calculation).
t is the number of years the money is invested or borrowed for.
In this calculator, we simplify this by directly using the daily rate within the calculation, assuming 365 compounding periods per year. The effective daily rate is (annual rate / 365).
Why Daily Compounding Matters
The key advantage of daily compounding is its frequency. The more often interest is compounded, the faster your money grows (or debt accumulates). Even a small difference in compounding frequency can lead to substantial differences in the final amount over long periods. For savings accounts, bonds, and other investments, daily compounding maximizes your earnings. Conversely, for loans or credit card debt, daily compounding means you'll pay more interest over time, highlighting the importance of paying down balances quickly.
Use Cases for This Calculator
Savings & Investments: Estimate the future value of your savings accounts, certificates of deposit (CDs), or investments that compound daily.
Loan Analysis: Understand how much interest you might accrue on a loan with daily compounding, such as certain types of short-term loans or credit card debt.
Financial Planning: Project the growth of your wealth over time for retirement planning or other long-term financial goals.
Comparing Financial Products: Evaluate different savings or loan offers based on their compounding frequency and interest rates.
By using this calculator, you can gain a clearer picture of how daily compounding impacts your financial outcomes, empowering you to make more informed decisions.
function calculateDailyCompoundInterest() {
var principal = parseFloat(document.getElementById("principal").value);
var annualRate = parseFloat(document.getElementById("annualRate").value);
var timeInYears = parseFloat(document.getElementById("timeInYears").value);
// Basic validation
if (isNaN(principal) || principal < 0 ||
isNaN(annualRate) || annualRate < 0 ||
isNaN(timeInYears) || timeInYears < 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
var dailyRate = annualRate / 100 / 365; // Convert annual rate to daily decimal rate
var numberOfPeriods = timeInYears * 365; // Total number of compounding periods
// Formula: FV = P * (1 + dailyRate)^numberOfPeriods
var futureValue = principal * Math.pow(1 + dailyRate, numberOfPeriods);
var interestEarned = futureValue – principal;
document.getElementById("displayPrincipal").textContent = "$" + principal.toFixed(2);
document.getElementById("displayInterest").textContent = "$" + interestEarned.toFixed(2);
document.getElementById("finalAmount").textContent = "$" + futureValue.toFixed(2);
}