Future Value (FV)
Present Value (PV)
Payment (PMT)
Calculation Result
Understanding the TI BA II Plus Time Value of Money Logic
The TI BA II Plus is the industry standard for financial analysts, CFA candidates, and business students. Its most powerful feature is the Time Value of Money (TVM) worksheet, which allows users to solve for one of five variables when the others are known. This calculator emulates that logic to help you perform complex financial modeling quickly.
The Five Key Variables
N (Periods): The total number of compounding periods (e.g., years, months, or quarters).
I/Y (Interest per Year): The annual interest rate. Note: This calculator handles the periodic conversion internally if you adjust N accordingly.
PV (Present Value): The current value of a sum of money or stream of cash flows. In financial terms, an outflow is usually represented as a negative number.
PMT (Payment): The amount of the annuity payment made each period.
FV (Future Value): The value of an investment or cash flow at a specific date in the future.
Common Use Case Examples
Example 1: Solving for Future Value (FV)
Suppose you invest 5,000 today (PV = -5000) at an annual interest rate of 7% (I/Y = 7) for 10 years (N = 10). By clicking CPT, the calculator determines how much your investment will grow to, assuming no additional payments (PMT = 0).
Example 2: Determining Required Savings (PMT)
If you want to have 1,000,000 (FV = 1,000,000) in 30 years (N = 30) with an average return of 8% (I/Y = 8), starting with nothing (PV = 0), this tool calculates the annual payment (PMT) required to reach that goal.
Standard Cash Flow Convention
Like the physical TI BA II Plus, this calculator follows the cash flow sign convention. If you are "paying out" money (an investment or deposit), enter it as a negative number. if you are "receiving" money (a loan received or a future payout), it is positive. If your result is negative, it simply means a cash outflow is required to satisfy the equation.
function updateUI() {
var solveFor = document.getElementById("solveFor").value;
document.getElementById("pvContainer").style.display = (solveFor === "PV") ? "none" : "block";
document.getElementById("pmtContainer").style.display = (solveFor === "PMT") ? "none" : "block";
document.getElementById("fvContainer").style.display = (solveFor === "FV") ? "none" : "block";
document.getElementById("resultsArea").style.display = "none";
}
function calculateTVM() {
var solveFor = document.getElementById("solveFor").value;
var n = parseFloat(document.getElementById("nVal").value);
var rate = parseFloat(document.getElementById("iVal").value) / 100;
var pv = parseFloat(document.getElementById("pvVal").value);
var pmt = parseFloat(document.getElementById("pmtVal").value);
var fv = parseFloat(document.getElementById("fvVal").value);
if (isNaN(n) || isNaN(rate)) {
alert("Please enter valid numbers for N and I/Y.");
return;
}
var result = 0;
var resultLabel = "";
try {
if (solveFor === "FV") {
// FV = PV*(1+r)^n + PMT*[((1+r)^n – 1)/r]
if (rate === 0) {
result = -(pv + (pmt * n));
} else {
result = -(pv * Math.pow(1 + rate, n) + pmt * (Math.pow(1 + rate, n) – 1) / rate);
}
resultLabel = "Future Value (FV)";
} else if (solveFor === "PV") {
// PV = [FV / (1+r)^n] + [PMT * (1 – (1+r)^-n) / r]
if (rate === 0) {
result = -(fv + (pmt * n));
} else {
result = -(fv / Math.pow(1 + rate, n) + pmt * (1 – Math.pow(1 + rate, -n)) / rate);
}
resultLabel = "Present Value (PV)";
} else if (solveFor === "PMT") {
// PMT = [FV + PV*(1+r)^n] * [r / (1 – (1+r)^n)]
if (rate === 0) {
result = -(fv + pv) / n;
} else {
result = -(fv + pv * Math.pow(1 + rate, n)) * (rate / (Math.pow(1 + rate, n) – 1));
}
resultLabel = "Payment (PMT)";
}
document.getElementById("resultsArea").style.display = "block";
document.getElementById("resultText").innerText = resultLabel + ": " + result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("summaryText").innerText = "Calculation based on " + n + " periods at " + (rate * 100).toFixed(2) + "% interest.";
} catch (e) {
alert("Calculation error. Please check your inputs.");
}
}