Understand how the value of money changes over time. Use this calculator to see the future value of a present sum or the present value of a future sum.
Future Value of Present Sum
Present Value of Future Sum
Calculation Results
Future Value:—
Present Value:—
—
Understanding the Time Value of Money
The concept of the Time Value of Money (TVM) is a fundamental principle in finance stating that a sum of money is worth more now than the same sum will be at a future date due to its potential earning capacity. This is based on the idea that money can be invested and earn interest over time, thus growing in value.
Why is TVM Important?
Investment Decisions: It helps in evaluating whether to invest in one project over another by comparing the present value of expected future returns.
Loan Evaluation: Understanding TVM is crucial for lenders and borrowers to determine the true cost of borrowing or the yield on lending.
Retirement Planning: It allows individuals to estimate how much they need to save today to meet future financial goals, such as retirement.
Business Valuation: Businesses use TVM to discount future cash flows to their present value, which is a key component in determining a company's worth.
The Math Behind the Calculator
Our calculator uses standard TVM formulas. The core idea is that money grows with compounding interest. The formulas involve:
Present Value (PV): The current worth of a future sum of money or stream of cash flows, given a specified rate of return.
Future Value (FV): The value of a current asset at a specified date in the future on the basis of an assumed rate of growth (interest rate).
Interest Rate (r): The rate at which money grows per period. In our calculator, this is the annual interest rate.
Number of Periods (n): The number of compounding periods. In our calculator, this is the number of years.
Future Value Formula:
The formula to calculate the future value of a present sum is:
FV = PV * (1 + r)^n
Where:
FV is the Future Value.
PV is the Present Value (the `Current Amount` you input).
r is the annual interest rate (expressed as a decimal, e.g., 5% becomes 0.05).
n is the number of years.
Present Value Formula:
The formula to calculate the present value of a future sum is derived from the future value formula:
PV = FV / (1 + r)^n
Where:
PV is the Present Value.
FV is the Future Value (the `Future Amount` you input).
r is the annual interest rate (expressed as a decimal).
n is the number of years.
How to Use This Calculator
1. Select Calculation Type: Choose whether you want to find the Future Value of a Present Sum or the Present Value of a Future Sum.
2. Input Values:
If calculating Future Value, enter the Current Amount, Annual Interest Rate, and Number of Years.
If calculating Present Value, enter the Future Amount, Annual Interest Rate, and Number of Years.
3. Calculate: Click the 'Calculate' button.
The results will show the calculated Future Value and Present Value based on your inputs.
function toggleInputs() {
var calculationType = document.getElementById("calculationType").value;
var presentSumSection = document.getElementById("presentSumSection");
var futureSumSection = document.getElementById("futureSumSection");
var fvResultDiv = document.getElementById("futureValueResult");
var pvResultDiv = document.getElementById("presentValueResult");
if (calculationType === "futureValue") {
presentSumSection.style.display = "block";
futureSumSection.style.display = "none";
fvResultDiv.style.display = "block";
pvResultDiv.style.display = "none";
} else { // presentValue
presentSumSection.style.display = "none";
futureSumSection.style.display = "block";
fvResultDiv.style.display = "none";
pvResultDiv.style.display = "block";
}
// Clear previous results when type changes
document.getElementById("fvResultValue").textContent = "–";
document.getElementById("pvResultValue").textContent = "–";
document.getElementById("finalResult").textContent = "–";
}
function calculateTimeValue() {
var calculationType = document.getElementById("calculationType").value;
var annualInterestRate = parseFloat(document.getElementById("annualInterestRate").value);
var numberOfYears = parseInt(document.getElementById("numberOfYears").value);
var finalResultElement = document.getElementById("finalResult");
var fvResultValueElement = document.getElementById("fvResultValue");
var pvResultValueElement = document.getElementById("pvResultValue");
// Clear previous results
fvResultValueElement.textContent = "–";
pvResultValueElement.textContent = "–";
finalResultElement.textContent = "–";
// Validate inputs
if (isNaN(annualInterestRate) || isNaN(numberOfYears) || numberOfYears < 0) {
finalResultElement.textContent = "Please enter valid numbers for Rate and Years.";
return;
}
var rateDecimal = annualInterestRate / 100;
if (calculationType === "futureValue") {
var presentSum = parseFloat(document.getElementById("presentSum").value);
if (isNaN(presentSum)) {
finalResultElement.textContent = "Please enter a valid Current Amount.";
return;
}
var futureValue = presentSum * Math.pow(1 + rateDecimal, numberOfYears);
fvResultValueElement.textContent = "$" + futureValue.toFixed(2);
finalResultElement.textContent = "Your investment will grow to $" + futureValue.toFixed(2) + " in " + numberOfYears + " years.";
document.getElementById("results").style.display = "block";
} else { // presentValue
var futureSum = parseFloat(document.getElementById("futureSum").value);
if (isNaN(futureSum)) {
finalResultElement.textContent = "Please enter a valid Future Amount.";
return;
}
var presentValue = futureSum / Math.pow(1 + rateDecimal, numberOfYears);
pvResultValueElement.textContent = "$" + presentValue.toFixed(2);
finalResultElement.textContent = "You would need $" + presentValue.toFixed(2) + " today to have $" + futureSum.toFixed(2) + " in " + numberOfYears + " years.";
document.getElementById("results").style.display = "block";
}
}
// Initialize on page load
document.addEventListener("DOMContentLoaded", toggleInputs);